Jigsaw Puzzle World

Completing the same puzzle multiple times counts and you can turn it into a 4 piece sliding puzzle, which is trivial. It takes just a few seconds each and you should be able to get this along with all the other achievements in 15 minutes if you start using this strat immedietly.

There is also Steampunk Jigsaw Puzzles which is the same game with different images if you want more free TSA.