Here is the full list of all 11 Hexologic achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Complete all special levels
Complete 60 basic and 15 special levels
Complete 90 basic and 21 special levels in hard mode
Complete special levels of Forbidden Planet
Complete 60 basic levels
Complete 90 basic levels in hard mode
Space Master
Complete sky special levels
Complete underwater special levels
Complete jungle special levels
Complete desert special levels