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