Let's start with an etymology lesson. The slang term "mobs" as used in online games is short for "mobile objects". It originally meant, anything that moves and isn't a player. It has come to mean, any monsters that you fight. One mob is one monster, not a group of monsters. Now that half of the people who clicked this link have already left, let's get back to what the title promised.
There are many different types of monsters in this game, and they require different strategies. Charging in headstrong with a sword and hacking away without any concern for your own safety usually isn't a viable strategy. Rather, different mobs take different strategies to kill them without getting hit. I'm here to explain the strategies.
Beasts: (vulnerable to piercing damage, resistant to elemental damage)
Chromalisks:
These attack pretty slowly, and give you plenty of warning. It usually isn't hard to get in melee range and hack away, and often, you can do a full sword combo. Do back off if you see the colored spikes in front of one that indicates that it is going to attack. Plain chromalisks merely stick out their tongue, so all you have to do is dodge. Some other types spit at you, and if the spit hits you, or if you step on it, it will inflict a condition on you. That means you have to dodge the original attack, and also not step on the spit. This isn't hard, though, at any tier.
Wolvers:
These also attack slowly, and give you a lot of warning. They're most easily killed with a sword, as they're pretty agile and can dodge ranged attacks pretty well. You can often pick out a wolver and hack away until it dies, even if it takes three sword combos to kill it. Do back off if you see the colored spikes that warn that they're going to attack. Wolvers leap ahead and bite, so if one is attacking, you don't want to be right in front of it.
At tier 3, wolvers gain a teleport move. If you see that a wolver is going to attack, even if you're not right next to it, you should be wary that it might teleport to you and then attack. When no wolver is preparing an attack, it's safe to hack away at whatever is there.
Alpha wolvers:
These are the big wolvers, and kind of a mini-boss. As with normal wolvers, they attack slowly, and give plenty of warning. Rather than a single lunge and bite, however, alpha wolvers do three in a row. Furthermore, their bites hurt. Blocking an alpha wolver is no good, as they'll break right through your shield. Rather, when you see an alpha wolver preparing an attack, you have to run away, immediately.
You can charge in and attack an alpha wolver with your sword, like any other wolvers. But you have to watch to see if they're going to attack, and run away if immediately when you see that an attack is imminent.
Most alpha wolvers come just one at a time in arena-like areas just after a party button. These have a lot of health, too. Alpha wolvers gain the teleport move at tier 2. Watch to see who the alpha wolver is attacking, and if you're in a full group and it's coming after you, then it's okay to just be cautious and dodge while your teammates kill the other mobs. You really don't want the alpha wolver to teleport right to you and hack away, as that really hurts.
There are some places where you'll have to fight several alpha wolvers at once. These only have normal mob health. Be careful, and be quick to back off. Heavy guns like the magnus line can interrupt alpha wolvers, so they're pretty effective.
Constructs: (resistant to piercing damage, vulnerable to elemental damage)
Rocket puppies:
These shoot missiles. In tier 1, the missiles fly straight, so you can dodge them and attack the rocket puppy. In tiers 2 and 3, the missiles will curve to chase you. Sometimes you can make them chase you into other mobs and damage the other mobs. Often you'll have to simply put your shield up and absorb the blow as best as you can. In the latter case, try to hack away and kill the rocket puppy as quickly as you can, even if you have to take some damage to do so. If you can time it right, the end of a sword combo will interrupt their attack.
Red rovers:
These shoot fire paths. You mostly have to dodge their shots, as the fire stays on the ground for a while. Get in melee range and run around when they're going to attack, and they'll miss you. That gives you an opening to hack away with a sword and kill it.
Other gun puppies:
At tier 1, these shoot a single projectile. At tier 2, they shoot three in a spread pattern. At tier 3, they shoot five consecutively in a spread pattern, and not all simultaneously. Higher tiers make it harder to dodge, but don't change the strategies.
Gun puppies sometimes take a while to recognize that you're they're and attack. If a gun puppy is inactive, sometimes you can charge your sword while out of combat, and then start combat with a charged sword attack against a gun puppy. Otherwise, you can often just hack away in melee. The end of a sword combo will interrupt a gun puppy, but you can't always time this right. If a gun puppy opens its mouth to attack, then block its attack, and then you can go back to attacking with your sword.
Gun puppies are also easy to kill with a gun, as they don't move. Some gun puppies are in places that are hard to reach in melee, meaning that you should kill them with your gun. You have plenty of time to fire off a full volley from your gun, then dodge the retaliatory attack, then fire again, and so forth. Put your shield up while trying to dodge a gun puppy, in case you're unable to dodge, but also try to get out of the way.
Another important thing to note about most gun puppies is that you don't need to fight other mobs near them. If there are gun puppies in an area, and also other mobs, then you can back off and the other mobs will chase you. The gun puppies can't, so you can kill the other mobs by themselves, without being harassed by gun puppies.
Lumbers:
These attack slowly, but they have a fairly long melee attack, and they hit hard. They also don't give you that much warning before they attack. The move and rotate slowly, so the best defense is to stay out of their line of fire. In most cases, lumbers are most easily killed with guns. If they never get within range of you, then they can't damage you.
If you have to melee a lumber, then put your shield up and run around it in circles. At some point, double back and start running around it in the opposite direction. That will get the lumber to swing at you as you go by, and miss. After a lumber attacks and misses, you have time to land a lot of attacks before it can recharge and attack again. In tier 3, a typical 3-hit combo sword will let you safely do a full combo plus an extra two hits if you attack right after a lumber does.
Do not charge your sword against lumbers while you are in a group, as this can knock them long distances. Even if you don't get hit, this quickly moves a lumber to a spot that your teammates weren't expecting, and the lumber might immediately smash one of them. Lumbers hit hard, and can often break a shield in a single hit. Losing 12 lines of health because one of your teammates is an idiot who wants to knock lumbers around is not fun.
Mecha knights:
These tend to come in large groups. If several are following you, then bombs are the most effective way to attack them. You can run around while charging a bomb, then drop it, and make them chase you across it and get hit. Starting in tier 2, they'll block a lot of gun attacks, but won't block sword or bomb attacks unless they're trying to block someone else's gun attack.
If you're fighting one mecha knight by itself, then you can run in, whack it once or maybe twice with a sword, then shield and run. You may sometimes need to shield bump a mecha knight to get it off of you, or put your shield up to absorb one of their charged sword attacks. The latter will knock you a considerable distance, so make sure you're pointed in a direction that it is safe to go.
Retrodes:
Retrodes will try to melee if you're in melee range. Starting in tier 2, these get a beam attack, which is what they'll use if you're not in melee range. Retrodes give a lot of warning before their beam attack, by tossing their heads back as if preparing to sneeze. Get out of the way of their beam attack.
Retrodes are most easily killed with a gun. They're fairly slow, so it's easy to stay out of melee range. In tier 2, if you get out of the way when a retrode uses its beam attack, you can fire off two full gun combos before the retrode can recharge the beam attack and use it again. In tier 3, you only have time for one full combo.
Note that the retrode beam attacks do not go past anything that you can't run across. This means that barriers that block you, but not your gun shots, will block retrode beam attacks. In some cases, it's possible to stand on one side of such a barrier and fire away at a retrode, while it can't do anything to do you because the barrier blocks its beam attack.
Scuttlebots:
These move slowly, attack slowly, and have a short enough range that they're basically melee. If you're in melee range and one is attacking, then block. Other than that, hack away by with a gun or sword as you prefer.
Fiends: (vulnerable to piercing damage, resistant to shadow damage)
Devilites:
"Normal" devilites will throw things at you. They can snap off an attack very fast, so you need to keep your shield up even when you don't see an attack coming. If you wait until you see one raise something to throw, it's too late. You should also move back and forth some, so that you'll dodge naturally dodge a lot of their attacks, even without intentionally reacting to a particular attack.
Normal sword attacks interrupt these devilites. You can keep your shield up while moving into melee range, then attack once, and then immediately put your shield back up. If you're only fighting one or two devilites, you can usually kill them without getting hit this way. If you're fighting larger groups, then try to split them up.
Devilite overtimers have two attacks. One is a melee axe attack that they give a fair bit of warning for. You can get out of the way, and then attack it when it misses. The other attack is a pitchfork that they don't give much warning for. These hit pretty hard, so you don't want to have to fight multiple overtimers at the same time if you can help it.
Devilites can also be interrupted by the magnus line of guns. They're pretty agile, so a lot of other guns are ineffective.
Pit bosses and yesmen do not attack at all. If you kill a pit boss, then sometimes one or more other devilites will be promoted to pit boss and stop attacking you. On the other hand, if you kill a pit boss near a yesman, sometimes the yesman will turn hostile. If you leave pit bosses and yesmen for last, then you should be aware that as soon as you kill all of one, then all of the other will turn hostile. Try to get it down to one of each before killing the last of either type.
Greavers:
These will use a dive attack with colored lines to warn that they're going to attack. Starting in tier 2, they'll leave a cloud on the ground that inflicts a condition if you step in it. The condition is unblockable, so it can affect you even if your shield is up. Starting in tier 3, greavers will also shoot in four directions immediately after their dive attack.
A greaver's dive attack can be interrupted by a normal sword attack, and this stops their whole combo of moves. For a single greaver, hack away with your sword until it dies. For multiple greavers, try to spread your attacks to interrupt them all, or run to teammates for help. You can't dodge their dive attack, as they're faster than you and will chase you down. You can only partially block it, as the condition will go right through your shield. You can try to shield bump them away if overwhelmed.
Trojans:
These have an attack buff area attack. Shield up and back away when you see one flex to use this. They also have a charge attack, and an overhand sword attack. They give some warning before either of these, but they both have pretty long range and hit hard. They'll only use the charge or sword attack if you stop for a while so that they can line up and attack.
Trojans are only vulnerable from behind. The ideal way to kill one is to have multiple people standing on opposite sides of the trojan. If it faces one of them, then that one moves back and forth to prevent the trojan from using any attack, while the other hacks away with a sword from behind. If the trojan turns around, then the two players switch roles.
If you have to fight a trojan solo, then bombs work well. Run in circles around the trojan, drop a bomb, and then make sure that you're standing on the opposite side of it when the bomb explodes. That will hit and damage the trojan.
Trojans nearly always drop hearts when they die, and often several hearts.
Trojans will damage other mobs, too, and not just players. In some spots, this can be useful as a way to get a trojan to kill other mobs so that you don't have to fight them.
Wings:
These are the butterfly healer mobs. They won't attack you, but they will heal other mobs. They tend to hold still until they see something to heal, then fly to it and heal. Because wings tend to be near other mobs, the main danger in attacking them is being hit by the other mobs. Tactics to use depend on what the other mobs are.
Gremlins: (vulnerable to shadow damage, resistant to elemental damage)
Thwackers:
In tier 2, these get a two attack sword combo. In tier 3, these get a shield on their back so that they can only be damaged from the front.
Guns are pretty effective at taking out thwackers. They'll jump back if you use a gun, which also keeps them off of you pretty effectively. Thwackers sometimes come in large groups, so if you have to attack a group, be careful to hit once and run, and not get surrounded and let them hack away at you.
The key to fighting thwackers with a sword is to attack faster than they do, which means you need a fast sword. The flourish lines are pretty effective. The calibur and brandish lines are just too slow to work very well.
Scorchers:
These mainly use a flamethrower attack to leave fire on the ground. Occasionally they'll shoot bullets at you. These are pretty slow and can wander aimlessly. It's often easy to get one by itself, and then hack away with a sword until you kill it. If there are too many of them together, then back off, and they'll probably spread out. Scorchers don't chase much like thwackers do.
Demos:
These plant bombs on the ground, and can throw bombs at you, which then go on the ground an explode. They're a pain to melee, as you likely step on the bombs and get hit. They're easier to shoot with guns, even though they dodge a lot. It's often best to take out other gremlins or other mobs first, and leave the demos for last.
Menders:
Menders will occasionally shoot their ember bolt attack at you, but mostly they heal other mobs. They're pretty effective healers, so it helps to kill them so that you can kill other mobs. In tier 2, they get an area heal. In tier 3, they get an energy dome that makes them invulnerable until you break it. In tier 3, they also learn to revive other mobs, though they don't use this very often.
If you can get a mender by itself, then you can hack away with your sword until it is dead. A sword will knock the mender back some, and it will also jump back to try to dodge your sword. You can use this to push the mender away from other mobs and kill it. If a mender uses its energy dome, that will stop the knockbacks, so while you can hack away and break the dome, you may need to be wary of other mobs coming to attack you. You usually want to pick off menders by themselves, to stop them from healing other mobs.
Slimes: (vulnerable to shadow damage, resistant to piercing damage)
Jellies:
Against most jellies, you want to charge in, swing your sword twice, and then shield up and back away. That way, you'll avoid the counterattack. If your first sword swing misses, or the two sword swings hit two different mobs, then still, don't try to get a third attack in. This works with large groups of jellies, too, and not just individual ones.
If you're far away, jellies may use a ground spike attack. In that case, try to get off of the ground spikes, but put your shield up in case you fail to do so.
Blast cubes:
These can be fought the same as other jellies, except that once killed, they wait three seconds and then explode. Get out of the way so as not to be caught in the explosion.
Lichens:
Lichens are most easily attacked with a sword. Hit one swing short of a full sword combo and then stop, and then again once swing short of a full combo and then stop, and so forth. If you see the red spikes that mean a lichen is about to attack, then put your shield up. The problem with finishing a full sword combo is that there is a considerable delay before you can shield again, which leaves you vulnerable, even though you can often get a full combo off safely against lichens.
The other key thing against lichens is that sword attacks knock them a considerable distance. You want to knock them away from each other so that they can't combine.
Lichen colonies:
These can be fought just like lichens when you're attacking the mob itself. They attack faster than normal lichens, so you'll have to stop to shield more often. Beware that lichen colonies can fire spikes long distances, which can hit you while you're trying to fight other mobs. Guns can be pretty effective against lichen colonies, too, though be aware that if you finish a full gun combo, you might not be able to put your shield back up in time when you need to.
Giant lichen colonies:
These can be fought much like lichen colonies, even though they gain a ground spike attack. Only try to get one or two attacks in before you put your shield up, as they attack pretty fast. If your shield takes too much damage, then run away and dodge for a while while your shield recharges.
Oilers:
Try not to light these on fire. If you don't light them on fire, then fight them like jellies. If you do light an oiler on fire, then you have to be cautious and not step where an oiler has just been, as it will sometimes leave fire on the ground and burn you. In particular don't try multiple consecutive swings from a sword that makes you move forward to thrust.
You can put out an oiler's fire by freezing it. If you're going to fight oilers, then having a freeze bomb is very useful.
Quicksilvers:
The main thing here is don't shock them. If not shocked, then fight quicksilvers like jellies, with two sword attacks and then back off. If a quicksilver does get shocked, then put your shield up and wait for the shock to wear off.
Toxigels:
In tiers 1 and 2, you can fight these like lichens, though without worries that they combine. In tier 3, they gain an attack to shoot spikes. They give a lot of warning before they fire, but you need to back off and put a shield up when one is about to fire.
Toxilargos:
These aren't common, but fight roughly like giant lichen colonies. They also leave a considerable poison area on the ground that will poison you if you stand on it. As such, these are most easily killed with guns and not swords.
Undead: (vulnerable to elemental damage, resistant to shadow damage)
Kats:
These will lunge and then attack immediately after they lunge, and then sit there and not move for a while. If they see something in melee range, they'll try to bite for their attack. If not, then they'll shoot bullets in your direction. In higher tiers, they offer far less idle time between attacks.
The key to fighting kats is to wait for them to attack, and try to dodge their attack. Keep your shield up, in case you fail to dodge. After a kat attacks, then it can't attack again for a while, so it's safe for you to run in and hack away with a sword.
With just one kat, this is pretty easy. With two, it's still doable. For several kats at once, bombs work better. Run to an area with no kats while charging your bomb, and lay a bomb there. Then all the kats charge toward you and end up near the bomb, while you run away. The bomb blows up and a bunch of kats take damage. A freeze bomb also works well, as if you stop some kats from moving, it's easier to pick off and kill another one while it is by itself.
Zombies:
Zombies have a melee swipe attack, a leaping toward you attack, and a breath attack. The breath attack will be interrupted if the zombie takes damage. Zombies move slowly, so it's usually pretty easy to stay out of their range and shoot them with a gun. If zombies can never get close to you, then they can't damage you.
Zombies are also pretty easy to melee, if you want to kill them more quickly. Slash once with a sword, then get out of the way of the counter attack, then move in to attack again, and so forth. If you move in quickly enough after a zombie attacks and misses, you can safely get in two sword slashes. If a zombie does a jump or breath attack, or isn't facing you, you can also get in two sword slashes.
Note that zombies will revive if killed near a grim totem. Pull zombies out of the way of totems before fighting them. In some cases, you'll have to move totems so that you can get ample room for zombies to be out of range of the totems.
Phantoms:
Run away, as phantoms cannot be killed. All that you can do is disable them for a while before they come after you again. You can't outrun a phantom, and they'll break a shield pretty quickly in tier 3, so they're pretty nasty to fight.
If you're trying to clear a graveyard level, then you'll have to deactivate phantoms for a while on various occasions. Pull them well away from zombies in order to fight them alone. Shooting phantoms with guns is pretty effective. When a phantom charges its sword, run in circles around it until it misses. It won't attack again for a while, which gives you plenty of time to land a full sword combo. Don't start attacking too quickly or you could run into the sword blades from behind and damage yourself.
Couple of things that might be useful to add, in no particular order.
Blast cubes (at least at t2 and t3, never seen one in t1) will explode into smaller pieces which will bounce a short distance, flash, and explode. Like the big explosion, the smaller ones can damage you and other mobs.
Gremlin Menders: Not entirely sure if this is a bug or not, but I've noticed that they aren't weak to shadow most of the time (might just be the fact that I'm using a nightblade.) and are resistant to pierce. Need to test this further, but maybe others have seen it happen too.
Phantoms: They have the charge attack of a Faust, so be careful even if you've got some distance on them. You can tell if they're targeting you if you have small black/purple ring of arrows around your feet (same goes for rocket puppy missles).
Kats only shoot bullets starting in t2.
Thwackers (t2 and up?) will throw their axe at you if far enough away.
Yesmen only turn into overtimers if there are no more pitbosses left, pitbosses turn into regular devilites if they have no more lackeys left.
Don't shield against alpha wolvers, they'll probably break it and you'll end up taking damage. Much better to do as you've said and move back.
And typically with chromalisks, you can continue to attack them, just circle around so you're not directly in front once the attack indicator starts.
Very useful guide though.