At the title screen, press rapidly. After 10 button presses the credits will increase by 1. Make sure you move the cursor up or down or the demo will start and the credits will be reset to 4 when you return to the menu. You can increase your amount of credits/continues to a maximum of 9.
Insane demo screen
Random Weapon Select
To find out on how to acsess the stages, see the walkthrough of the stages. The bonus stages are similar to the MSX Gradius' bonus stages.
Cube Attack Mode
To try the last part of stage nine, beat stage 9 in order to unlock this mode in "Extra Mode" .
At the final boss, if you get hit by the bottom energy ball, you play a bonus stage based off the first stage of Gradius. Acsess that to unlock this in "Extra Mode".
At the final boss, if you get hit by the top or middle energy balls, you get sent to a bonus stage based off the latter half of stage 1 from Salamander. Acsess that to unlock this in "Extra Mode".
To unlock this, you must beat the game. This allows you to select ALL weapons, plus some from the SNES game. This is also in "Extra Mode".