Here is the full list of all 12 Hanoi Puzzles: Flip Match achievements.
Complete Level 1
Complete Level 10
Complete Level 20
Complete Level 30
Complete Level 40
Complete Half of the game with any number of moves
Complete Half of the game within the number of moves suggested
Finish the game with any number of moves
Complete the game within the number of moves suggested
Solve a level with less moves than the sugested
Solve at least 5 levels with less moves than the sugested
Complete the game in Challenge Mode