Here is the full list of all 20 PUZZLE: BIRDS achievements.
Finish Level 11
Finish Level 10
Finish Level 9
Finish Level 8
Finish Level 7
Finish Level 6
Finish Level 5
Finish Level 4
Finish Level 3
Finish Level 2
Finish Level 1
Finish Level 12
Finish Level 13
Finish Level 14
Finish Level 15
Finish Level 16
Finish Level 17
Finish Level 18
Finish Level 19
Finish Level 20