On Xevious 3D/G's main menu, highlight "Start" and then hold the following buttons to change the ship to various secret characters. Be sure to keep holding the buttons while the game is starting, until the ship changes and you can control it.
Dark Solvalou - L1, L2, R1, R2, SELECT, and START.
Heihachi (Player 1 only) - LEFT, CIRCLE, X, SELECT, and START.
Paul (Player 2 only) - RIGHT, CIRCLE, X, SELECT, and START.

When choosing Xevious 3D/G on the main menu, hold L2 while rapidly pressing CIRCLE. The faster it is pressed, the more credits that will be added. If it is pressed fast enough, there will be infinite credits.

Finish Xevious 3D/G on any difficulty level to unlock extra options on the main menu.