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