Here is the full list of all 20 Island Maze achievements.
Unlock level 5
Complete level 2 with 3 stars
Complete level 1
Unlock level 10
Unlock level 15
Unlock level 20
Unlock level 25
Unlock level 26
Unlock level 27
Unlock level 28
Complete level 8 in 17 moves
Complete level 16 in 40 moves
Unlock 8 secret levels
Unlock 20 simple levels
Collect 84 stars
Complete all levels
Collect 20 stars
Collect 40 stars
Collect 60 stars
Complete level 16 in another path