Here is the full list of all 32 My Jigsaw Adventures - there are A Lost Story achievements.
Complete one puzzle with 220 pieces
Complete the fourteenth special puzzle
Complete the fifteenth special puzzle
You unlocked the hidden puzzle. Play it in the Special section, puzzle 16.
Complete the thirteenth special puzzle
Complete the twelveth special puzzle
Complete the eleventh special puzzle
Complete the tenth special puzzle
Complete the nineth special puzzle
Complete the eighth special puzzle
Complete the seventh special puzzle
Complete the sixth special puzzle
Complete the fifth special puzzle
Complete the fourth special puzzle
Complete one puzzle with 90 pieces (special mode)
Complete the third special puzzle
Complete the second special puzzle
Complete one puzzle with 60 pieces (special mode)
Complete the first special puzzle
Complete all the story
Complete the fifteenth story puzzle
Complete the tenth story puzzle
Complete the fifth story puzzle
Complete one puzzle in Challenge mode
Complete one puzzle with 112 pieces
Complete one puzzle using the arrow shape
Complete one puzzle using the mozaic shape
Complete the first story puzzle
Complete one puzzle usign the traditionnal shape
Complete one puzzle with 28 pieces
Complete five puzzles in Challenge mode
Complete ten puzzles in Challenge mode