Here is how to skip the entire second world, and about half the game.

After completing the first level, you're supposed to press the confirm button. (J or Z) Instead, press the confirm button 2 times in quick succession, then twice again about a half second later. (The next screen will not be fully uncovered.) Pressing it too many times may cause the game to crash and your file will be reset. If it goes correctly, a still image of the credits world will appear. This is where time ends, but the game will have to be refreshed to move.

This is easy after practicing, and so far is the biggest trick in the Any% run.