Here is the full list of all 16 Gnome Enchanted Jigsaw Puzzles achievements.
Open level 1
Open level 2
Open level 3
Open level 4
Open level 5
Open level 6
Open level 7
Open level 8
Open level 9
Open level 10
Open level 11
Open level 12
Open level 13
Open level 14
Open level 15
Open level 16