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 the Friend side puzzles
Solve all non-challenge puzzles in the appendix area
Reach the end
Cause a chain of paradoxes
Solve 200 puzzles
Cause another paradox
Become a wall
Enter yourself
Flip a box
Solve the Even side puzzles
Push against yourself
Enter a clone box
Cause a cycle
Solve all puzzles in 4 different areas
Cause a paradox
Solve a blue side puzzle
Use the area select in the hub
Experience recursion
Solve a red challenge puzzle