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