In the Japanese version, hold Up + Left + A and press Start then immediately hold Select at the title screen
During the ending, before the closing credits starts rolling, press and hold the Select and Start and keep on holding until the credits are over. If done correctly, you will receive a message from Red Falcon, vowing his revenge.
When you enter the Base 1 or 2 levels, you can shoot high while ducking. Hold Up on Controller 2 while Controller 1 is ducking. You will be ducking but your bullets will appear to go high. This may be hard to pull off yourself, so help is recommended.
At the title screen, press and hold Up, Left and the A button. While holding these buttons, press Start and immediately hold Select. If done correctly, the stage select screen should appear.