The Red Baron can only be defeated on level 25. The trick to defeating him is not to shoot him down. Allow the Red Baron to get behind you. He is usually the second bogey you see. Go into vertical climb, then when you hit the ceiling, go into a nose dive (the more vertical the better). The Red Baron will follow. Just before you hit the ground, pull up. The Red Baron, being under-powered, will crash ending the game.
Complete the game to unlock a special option for cheats in the "Goodies" screen. You can get a booster, become invincible, and have unlimited rockets and bombs. When you have booster and bombs both activated, hold [Boost], drop a bomb, and release BOOST. Your bomb will travel faster than a rocket, and will go long distances.