Here is the full list of all 16 Puzzle Box Palace achievements.
Solve the observatory puzzle
Fall down from the top of the observatory
Solve the parlor puzzle
Solve the library puzzle
Solve the dining room puzzle
Solve the dining room puzzle by pulling 6 or fewer levers
Fold the dining room in half
Start the game
Solve the music room puzzle
Complete the game
Solve the dining room puzzle by pulling 3 or fewer levers
Solve the library puzzle without pulling any levers
Solve the parlor puzzle without the back room moving more than 6 times
Solve the sliding puzzle in the music room in 100 moves or fewer
Collect all pages of grandpa’s letter
Collect all achievements