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