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