Here is the full list of all 11 A Symmetric Escape achievements.
Complete all puzzles in the tutorial section.
Enter the main puzzle area.
Solve a puzzle requiring symmetry.
Solve a puzzle requiring rotational symmetry.
Solve a puzzle requiring diagonal symmetry.
Solve a pair of linked puzzles.
Solve a puzzle which is on the floor.
Ascend the fully constructed tower,
Escape.
Complete all puzzles in the game.
Leave the main puzzle area.