At the title screen, hold Left and press A, A, A, Start.
Press X rapidly when the title screen appears.
Pause the game and press Up, Up, Down, Down, L, R, L, R, B, A, Start. This should give you all weapons except your special gun.
At the options screen, highlight GAME LEVEL and press A rapidly.
When you get to the level with toxic bubbles floating around, go to the very end of the level where you see enemies in bubbles coming out of 2 openings. Destroy everything coming from the bottom opening, then enter it. The rest of the level will dissolve and the bonus round will begin.
Random Weapon Select
At the weapon select screen, press X, Y, X, X, Y, Y, X, Y.
To self destruct, pause the game and press Up, Up, Down, Down, Left, Right, Left, Right, B, A, Start.
For a better demo, hold A when the title screen appears.