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