When you're trying to skip the dialogue scenes, don't just mash the jump button. That causes the images to slowly fade out. Instead, hit Escape (if you're playing on keyboard) or the back/options/select button (if you're playing on a gamepad.) That skips the dialogue entirely.

It's important not to hit it before the screen fades out to transition between worlds, though. If you do that, you'll actually be losing time, as it will pause the game to ask if you want to quit.