Here is the full list of all 14 Albert and Puzzle Mansion achievements.
Beat the game.
Complete Level 1 with 2 or fewer moves.
Complete Level 2 with 7 or fewer moves.
Complete Level 3 with 13 or fewer moves.
Complete Level 4 with 5 or fewer moves.
Complete Level 5 with 8 or fewer moves.
Complete Level 6 with 16 or fewer moves.
Complete level 7 with 14 or fewer moves.
Complete Level 8 in a single move.
Complete Level 9 with a single move.
Complete Level 10 with 11 or fewer moves.
Complete all 10 levels with the fewest moves possible.
Skip the intro cutscene.
Defeat 4 haunted armors with a single cube.