Here is the full list of all 6 TILE PERFECT achievements.
Complete the Magical Girl Platformer puzzle in under 333 moves.
Complete the Rhythm Penguin puzzle in under 90 seconds.
Complete the Streamer puzzle in under 8 minutes.
Completed all 3x3 Slide Puzzles.
Completed all 4x4 Slide Puzzles.
Briefly encountered the Magical Girl on the title screen.