A lot of us out here finished the game when it came out. Me, Shekar & Ajay. I suppose Ajay was the first to do it.
From your image, it seem like you'll have to get 1 piece from the next stage "Hunt" & one from "Leap of Faith". That would allow you to get the puzzle piece which is on the top most end. The one below it needs that bouncing goomba to be brought down to get it.
Here's how it works. Get the puzzle piece from "Hunt" level & the very first puzzle piece from the "Leap of Faith". Head back to your current level & stand near the puzzle picture. Re-arrange the puzzle in such a way that the part of the puzzle which has a brownish bridge, connects with the bridge on the top (where the goomba is walking). Make sure you align it properly. If you do this correctly it will allow the goomba to walk over it & fall down. Once that happens, run toward him & bounce on top of him to get the puzzle which is just above to exit door.
For the top most puzzle, Just connect both those puzzle pieces I mentioned to get earlier, it will form a big plank like bridge, align it to the existing bridge (where goomba walks), yet again. Run towards the other side & jump while you're on the edge & you should make it on the plank which has the next puzzle.