I will say it again because it doesn't hurt: there is a whole new world with 10+ NEW PUZZLES, but hidden. To unlock that world you have to LOSE the first level. "Try again" must appear on the screen when you lose. Once that happens you will hear the victory music. Go to the map and the new world will be unlocked.
I'm looking for feedback on those levels mostly, the rest of the game is pretty much the same as last DD.
EDIT: if you don't know how to lose the first level, here is a tip: keep poking the gray toad.