Game help thread ftw.
To get to world four, you have to get the Mini-Mushroom in the desert area right before the boss battle. Then just survive until you get to the boss, a mummy spiny type thing. x.x It's quite easy, the hard part IMO is trying to hit the boss without running into one of its spines or fireballs.
So, yeah, just beat the mummy spiny type thing and you'll go to the World 3 sign, but as Mini-Mario you'll fall through the crack and go to world four 8D