Here is the full list of all 30 Oscar & Gems: Puzzle Quest achievements.
Complete level 30
Complete level 29
Complete level 28
Complete level 27
Complete level 26
Complete level 25
Complete level 24
Complete level 23
Complete level 22
Complete level 21
Complete level 20
Complete level 19
Complete level 18
Complete level 17
Complete level 16
Complete level 15
Complete level 14
Complete level 13
Complete level 12
Complete level 11
Complete level 10
Complete level 9
Complete level 8
Complete level 7
Complete level 6
Complete level 5
Complete level 4
Complete level 3
Complete level 2
Complete level 1