I need to prepare for Tier 3, any help?

Hi ho, its your friendly idiot Dipeero here. I am getting ready to head on to Tier 3 and I need desperate help. What gear should I have? Here's what I have now:
I am a sword/handgun hybrid. I am elementally orientated, using ice weapons because of my affinity for ice.
My sword is the Iceburst Brandish, with one orb off the Blizzbrand, so that isn't a problem.
My handgun is currently the Cryotech Alchemer MK. II. I don't use it much, so that can be subject to change.
My helm and armor are the Solid Cobalt armor.
My shield is the Great Defender.
So, what do you guys, being the ones with brain cells, think?
Any input I'll be grateful for.
-Doofus. I mean Dippero.

I have a detailed sword guide written for players in your situation. In addition to explaining the basic concepts and comparing swords, it explains how to build a mixed sword-gun loadout. Some highlights for you:
* Even if you're currently 3-star, always plan your items in terms of the 5-star versions. Then you won't get trapped in alchemy lines that don't go anywhere.
* In this game, you almost always want to be carrying multiple damage types. Very rarely do you want to carry just one damage type. So your current plan of Glacius and Hail Driver is not good.
* The standard Cobalt/Defender armors/shield are some of the worst in the game. Do not pursue them any farther, even though you get the recipes for free. Switch immediately.
Weapons: I won't say that you shouldn't upgrade your current Brandish and Alchemer, however I will go so far as to say that the Fire Brandish is significantly better. The Shock Alchemer is also preferable, but the Freeze Alchemer is great regardless. You can take that how you like, but it's something to consider.
Don't specialize in one damage type. Elemental is great and all, but you're going to be useless against Gremlins and Beasts with that loadout. You should invest in Shadow and Piercing weapons. Consider a Flourish or a Snarble Barb as a Piercing weapon, or Spine Cone, which upgrades in to an amazing Piercing bomb. For Shadow, look in to Nightblade, Faust, or Umbra Driver. If you'd like to keep your Freeze theme going, Tundrus is an amazing gun to look in to.
Armor: Drop Cobalt completely. I'm not going to sugarcoat this because no one deserves to waste their money on Cobalt. The Cobalt set is the worst armor line in the game. Not one of the worst, but THE worst. Heck, even Almirian Crusader beats it, and that's pretty horrible too. Funny enough, Almirian Crusader is upgraded from Cobalt.
Anyway, consider investing in to Wolver if you'd like to keep defending against Piercing. Wolver also upgrades to Skolver, which fits a winter theme well if you're in to that. Skolver is also a DIRECT upgrade to Cobalt. However, as your first armor set you should mostly be looking in to Vog Cub (which is upgraded from Wolver) if you want to be offensive, or Grey Feather (upgraded from Magic) if you want to be defensive. There's quite a few others you should look in to if you're interested, but for now those two are the go-to starter armors.
Shield: Just like the set it comes from, Defender is pretty horrible. Luckily Defender is actually usable, but you still shouldn't waste your time. Like before, if you want to keep defending against Piercing, look in to the Barbarous Thorn Shield line, which is a direct upgrade to Defender.
On to the more important shields, consider investing in to an Owlite Shield and upgrading that- it's one of the best defensive shields a noobie can go for. Alternatively, go for Crest of Almire, which has the same status resistances as the Owlite Shield but can be obtained through Boss Tokens, making it a great alternative if you don't want to level up a new shield (just don't make Aegis!). If you'd like to cover the most ground, get a Grey Owlite Shield and a Dread Skelly Shield, which will give you resistances to the four main statuses (the important part here), then you can get new shields as you like (Barbarous Thorn Shield and Swiftstrike Buckler immediately come to mind).
I know all of this is a lot of investing, but it will be worth it in the end when you're not stuck with a bad shield and useless armor set, and you're actually able to fight almost any enemy you come up against.