Here is the full list of all 26 Paper Cut Mansion achievements.
Reach Floor5
Reach Floor4
Unlock Vending Machine
Reach Floor3
Unlock An Equipment Card
Die for the very first time
Unlock An Evidence Piece
Reach Floor2
Unlock Father Papotto
Gain A Medal
Defeat 10 enemies
Defeat the Hat Man
Die 10 times
Complete Normal mode
Complete Hard mode
Complete Very Hard mode
Unlock All 27 Endings
Defeat 100 enemies
Defeat 500 enemies
Unlock All Equipment Cards
Unlock All Evidence
Reach Floor6
Gain 1000 coins
Solve 50 locks
Solve A Riddle
Solve A Musical Lock