Invincibility
When you lose a life and the countdown starts, quickly press and hold Triangle, Select, and start.
- Submitted by Bryce

In the Hunt
When your last ship from your last continue is destroyed press in this code hold Triangle + Select. While holding these, press Start for five continues

Extra Continues
At the main menu press in this code hold Upper-Left + Select. While holding these, press Circle

Level Select
Press pause during the game, t;hen enter the following Hold down the triangle and R2 buttons. You will get an extra boost of speed.