Here is the full list of all 27 Jigsaw Puzzle World Memories achievements.
Complete all game images
Complete image 20 of any level
Complete image 19 of any level
Complete image 18 of any level
Complete image 17 of any level
Complete image 16 of any level
Complete image 15 of any level
Complete image 13 of any level
Complete image 12 of any level
Complete image 11 of any level
Complete image 10 of any level
Complete image 9 of any level
Complete image 8 of any level
Complete image 7 of any level
Complete image 6 of any level
Complete image 5 of any level
Complete any image of 784 pieces
Complete image 14 of any level
Complete image 4 of any level
Complete any image of 484 pieces
Complete image 3 of any level
Complete any image of 289 pieces
Complete image 2 of any level
Complete any image of 144 pieces
Complete any image of 64 pieces
Complete the first image of any level
Complete the border pieces for the first time