Here is the full list of all 25 Isles of Cubes achievements.
Buy your first ship
Collect All Stars on Island 1
Finish Island 1
Collect All Stars on Tutorial Island
Finish the Tutorial Island
Earn your first Gold
Play 10 Cards
Finish Island 2
Finish Island 3
Finish Island 4
Finish Island 5
Earn 100 Gold
Earn 1000 Gold
Buy your second ship
Buy your third ship
Buy your forth ship
Buy your fifth ship
Buy your sixth ship
Finish Island 6
Collect All Stars on Island 2
Collect All Stars on Island 3
Collect All Stars on Island 4
Collect All Stars on Island 5
Collect All Stars on Island 6
Beat the Game and collect all stars!