Successfully complete the Ski Patrol Chief challenge to unlock the Helidrop level.
Successfully complete the Do Not Enter challenge to unlock the Moon Gate level.
Press Z while jumping.
When on an area that has a bomb, jump immediately before it then land on it. This requires some practice. When timed correctly, you will be able to get a quick special move (such as A + Y + A) in for an extra 6,000 or so points. This is useful for beginners that do not have all of their equipment yet.