This achievement needs a bit of clarification. It says "all jigsaws complete", but you will find that completing each puzzle once won't net you this achievement.
You need to do each of the puzzles a total of SIX times. You need to complete the 60 piece, 250 piece and 330 piece variations of all puzzles in Classic Mode. You will then need to complete each 60 piece, 250 piece and 330 piece variation of the puzzle in Ikemen Mode.