Here is the full list of all 11 Hexologic achievements worth 1,000 gamerscore. It takes around 1-2 hours to unlock all of the achievements on Xbox One.
Complete 90 basic levels
Complete underwater special levels
Complete special jungle levels
Complete special desert levels
Complete special sky levels
Complete all secret sky levels
Complete 90 basic and 21 special levels
Complete 90 basic levels in hard mode
Complete 90 basic and 21 special levels in hard mode
Complete cosmic special levels
Complete special levels of Forbidden Planet