You get this achievement for solving the 16th jigsaw puzzle. You have to be level 4 (
i.e., solved at least 14 other puzzles) before this puzzle will unlock.
The good news is that if you choose to start the puzzle by clicking on the crossed-out Z rather than the "Go" button, you'll have unlimited time and don't have to deal with the zombies attacking you. Also, all of the pieces are oriented correctly, it's just a matter of figuring out where they go. At any time you can click on the circle with the puzzle piece below the main board to temporarily see the image you're trying to reconstruct (the other button will change the color of the background).
The bad news is that you have to solve an entire puzzle in a single sitting. If you quit out of a puzzle it will completely reset the next time you play.