From StrategyWiki, the free strategy guide and walkthrough wiki

[edit] Super Shortcut

The Wario Stadium is notorious for this shortcut, probably for how it's so advantageous for the player and how easy it is to execute; note that if you do this with people who don't know the shortcut, you're going to cause trouble. Start the race, with or without the boost (with it makes it harder to hit the shortcut), jump when you are getting really close to the left side wall and are at the peak of one of the bumps. You may want to angle out (move to the right side of the track) and then back in to make it easier. If done correctly you will simply hop over the edge, note that if you're jump isn't high enough (due to the location of the jump, or angle) you may crash while hopping the wall (you will bounce and lose all acceleration).

As soon as you land shroom into the right side wall and start a left facing slide (this is the harder part), hop once if necessary to hit the wall near the top of the little hill (in the middle or a little after it). Before jumping let the slide go like a kart-length before hitting the wall, jump when you get close to it just like you did on lap 1. Repeat for laps 2 and 3 to get a time easily under 30 seconds and possibly under 15.