Here is the full list of all 15 The Cursed Tower of Lust achievements.
Chris enters dungeon for the first time
Clear 1F with Chris
Clear 2F with Chris
Clear 3F with Chris
Clear 4F with Chris
Anita enters dungeon for the first time
Clear 1F with Anita
Clear 2F with Anita
Clear 3F with Anita
Clear 4F with Anita
Defeat Lab Experiment Ω01
Defeat Lab Experiment Ω02
Defeat Lab Experiment Ω03
Defeat Lab Experiment Ω04
Become Merchant's slave