Here is the full list of all 25 Flip achievements.
Earned 100 stars
Played again a level in Random Puzzles Mode
Finished the first level
Finished 10 levels
Finished 20 levels
Played at least one puzzle from each level
Finished at least one puzzle from each level
Earned 500 stars
Earned 1000 stars
Finished all Simple levels
Finished all Sided levels
Finished all Wired levels
Finished all Image levels
Did 1000 flips
Undid 1000 flips
Did 10000 flips
Undid 10000 flips
Played 1000 puzzles
Mastered the 9th level from Simple
Mastered the 3rd level from Simple
Mastered all the puzzles of the Simple type
Mastered all the puzzles of the Sided type
Mastered all the puzzles of the Wired type
Mastered all the puzzles of the Image type
Mastered all puzzles and finished the game completely