Here is the full list of all 22 Patrick's Parabox achievements.
Solve all puzzles
Solve all non-challenge puzzles in the appendix area
Solve the Even side puzzles
Solve the Oblong side puzzles
Solve the Friend side puzzles
Solve the One side puzzles
Solve 200 puzzles
Solve a blue side puzzle
Solve all puzzles in 4 different areas
Use the area select in the hub
Reach the end
Cause a chain of paradoxes
Cause another paradox
Become a wall
Enter yourself
Push against yourself
Flip a box
Enter a clone box
Cause a cycle
Cause a paradox
Solve a red challenge puzzle
Experience recursion