Here is the full list of all 14 Rainbow Jigsaw achievements.
Finish game at difficulty 1
Finish game at difficulty 2
Finish game at difficulty 3
Finish game at difficulty 4
Finish game at difficulty 5
Prepare 30 custom pictures
Finish built-in picture 5 times
Finish game 10 times
Finish custom picture once
Prepare 10 custom pictures
Finish custom picture 10 times
Finish difficulty 1 with minimus steps
Finish difficulty 2 with minimum steps
Finish custom picture 30 times