Here is the full list of all 38 Possession achievements.
Possess all possessable creatures in the game at least once.
Kill every creature in the game at least once.
ill (or possess) every creature on a level.
Make it to a level boss as a ghost, without possessing anyone.
Defeat a level boss using a body from an earlier level.
Make it through an entire level using only one body.
Make it to the surface, possessing only 10 creatures or fewer (one per level).
Make it to the surface without exiting any still-living bodies.
Make it to the surface without possessing any living humans.
Make it to the surface without possessing any living sapient creatures.
Make it to the surface without possessing any living non-humanoid animals.
Make it to the surface, possessing only corpses and map features.
Make it to the surface, possessing only undead, constructs, corpses or map features.
Make it to the surface without damaging or possessing any creature that's not already hostile towards you.
Make it to the surface without possessing any living ratlings.
Kill an enemy by exploding your body.
Kill an enemy with an explosion from a body that exploded because it was killed by exploding your current body.
Kill an enemy by knocking them into something.
Kill an enemy by knocking them into a pit.
Exit a body with full health.
Play 500 total turns as a ghost (across any number of playthroughs).
Possess your own dead body on the surface.
Possess 100 creatures (across any number of playthroughs).
Escape the Graveyard.
Make it to depth 5.
Make it to the surface.
Defeat the final boss.
Get another creature to kill the boss of the Graveyard.
Kill the boss of the Tombs as a mummy.
Kill something with an explosion from a barrel that got hit by a minecart.
Kill a tentacle by ramming into it after being slapped backwards by another tentacle.
Kill a ratling plumber with a methane explosion.
Have three tame dinosaurs at the same time (not including one you're riding).
Make it to the exit room of the tavern without killing anyone.
Digest the boss of the Swamp.
Kill the boss of the Demon Ruins without weakening it first.
Kill the boss of the Temple while possessing a worshipper.
Defeat the final boss while possessing a villager of some kind.