Red Spirits in Graveyard Level
I went solo today after reading how to do so on the forums. Didn't realize when grouped that you COULD go down another level! So I scoped out as far as I could go.
I wound up in a graveyard level. Tons of skeletons, fairly easy to kill, seemed like awesome loots for me!
But these insane red spirits show up on a regular basis. I can attack them and eventually they become just a red dot, but after a period of time they will reanimate and hunt me down. As soon as I got trapped in a room and 3 of them showed up in addition to the nasty surprises programmed for the location, I wound up dead.
Is there some way to perma-kill these spooks? Or are you just meant to make a mad dash through those levels?
As far as I've been able to tell they are immortal.
However occasionally I will kill one and it's red dot will disappear. If there were for example 6 Phantoms and this happened, there will not be 5 Phantoms, but still 6. So it is either a visual glitch or a new one just spawns.
Either way they drop no mats, heat or coins.
Use your shield. A lot. Once they do their 3-attack combo they are totally vulnerable. And while they are charging you can also smack them a few times. At lower levels they have no Faust-projectile from their charge attack so you can simply back up and they will miss.
Good luck.
There should normally be only one Phantom per player in the graveyard, unless this was changed recently. If you move quickly, you should be able to find everything, kill all the zombies, and make it out relatively easily.
They are immortal and will never die - in T1 and T2 they are relatively easy to kill. Also note that they can teleport, so even if you're running away from one, it may pop up right in front of you should you stray too far ahead. This isn't a case of a second phantom showing up, but is actually the first one coming back to give you a hard time.
Hope this helps!

The Phantom, sadly, is immortal. And in response to NegimaSonic, I can confirm that they do in fact revive, as I found out recently (Backtracked to check for missed supplies, killed Phantom at choke point, stepped over him later, he regenerated as I stepped over him and killed me. On the spot.)
Unless you're carrying bombs or some kind of gun that you can shield quickly with, the best option really is to run. He can easily be kited over bombs, and shooting while moving is always a plus.
Also, in answer to the second question, you can dash through the levels if the Phantom gives you a hard time, but otherwise it isn't much of a worry. Take your time, kill and loot everything and you'll be one happy treasure hunter.
how r u suposed to kill everything with 4 phantoms poking at ya?? ur shield dies basically after 1 attack. too many zombies too no way u can kill all of them before phantoms start killing you its frustating
If there are 4 phantoms, you must have 3 other teammates. What are they doing such that you die by yourself? Teamwork, people, teamwork.
Oh, by the way, for what it's worth, Phantoms are weak to elemental damage too. They also deal shadow back to you.
shadow defense...skelly shields and such if its really giving you a hard time. i personally like to lure the phantoms into areas i've been so when they get knocked out they 1 don't reanimate (thought they only did if you were sticking around) 2 takes em awhile to get back to you and 3 you can deal with them 1v1 which isn't bad at all.
trying to kill the phantoms with 20 other zombies on you is just a mess and it won't happen.
also, elemental damage pwns them hard, so use it. the avenger, or even a buuunch of guns you can kite them with
Yeah, went back again later and fought for a while, got graveyard again and this time I went nice and slow, things were really easy. Each time I heard him yell, I backed up to a clear spot and kited him around a little while.

Does he get stronger each time he revives, or is that just me?
He doesn't seem to get stronger. I spent a looooong time exploring a huge graveyard level, gathering all the crowns and heat that I could, and I must have killed that dude 20 times. It took 4 hits each time (using a Kamarin, in T2), so it was easy to tell that nothing was changing.
One helpful thing to note is that you'll usually hear a creepy scream when the spirit guy is on the move again. That should give you a heads-up, at least, if you're paying attention.
Graveyards can be extremely profitable to solo, but it's VERY slow-going, and you have to be very cautious. Don't activate more than two or three graves at once (meaning, don't spawn skeletons by walking over the mounds of dirt near tombstones!). Clear all skeletons ASAP. When you hear that telltale "SHRIIIEK!"
....it's phantom time. Kiting works well, if you have an alchemer. Elemental damage is a bonus against them. If not, bombs can work (kite in circles). Do NOT kite them in a straight line down a narrow corridor, as they are very fast moving, they can teleport, you never gain too much distance on them, and their projectile is insane and CAN reach you. Try to dodge them, go in circles, evasive maneuvers, yadda yadda. If you have a sword ... well, never tried it past t2, but also do-able, but love your shield, watch their patterns and only advance when you know they're in a (very) brief down period.
Or .... do what I do sometimes, decide the loot, heat, and crowns aren't worth the stress, and run for the elevator down as fast as your stubby little Spiral legs will carry you.
@JunKx
They most certainly do reanimate whether you're there to witness it happening or not. They merely follow you and appear at your new location, travelling as those little red orbs. It will happen as long as you remain in the graveyard, even if you run as fast as you can.
Some people argue that they don't revive, more just show up in their place, I don't know or care because its the same result.
You can't finish them off forever in either case, you either kill the ones following you and take your few minutes of peace, or you do whatever you can to distract them and run.