This trick is tough to pull but if you do it right it usually works.
On the hard Venom where you're fighting the StarWolf team, wait for one of them to chase you and then fly right at one of the pillars or the big dome in the middle. At the last possible second, pull the 'upside-down U-turn' move(the thing you do automatically if you reach the edge of All-Range mode). You'll automatically go through the pillar due to a quirk in the game, but the StarWolf guy chasing you will crash and die. Even if his life meter is full he'll die! Funny!
In the first level if you go through all the cement rings, Falco will say "Follow me fox!" and he will take take you through a water fall to fight a secret boss.
Space Warp-Speed Trick:
In the space level with the spinning rings. Fly through all the rings until you hit warp speed. Once this happens you can shoot the asteroids to get bombs and other power-ups, AND ....you'll skip the boss!
Fight Star Wolf in Training:
Go through training until you reach 3D mode. Then get 100 hits and a Star Wolf fighter will appear without shields. He will keep coming out every time you kill him.
Move the 64 symbol:FAQ
Turn on the game and wait for the Title screen to appear. Now wait for the characters to start talking move the Analog Stick around to move the 64 symbol.
Star Fox 64 - Astuces Soluces