As soon as you start on level one, fly to the bottom left corner of the screen and drop a bomb. You should hear a chime, indicating that you now have two extra lives.
When you see the Yellow Weapon Powerup, hold Select and pick it up. If done right, your weapon will have homing abilities.
While playing, first lose all your lives and continues. Then, when the words "Game Over" appears and before it goes back to the title screen, press II, I, II, II, I, I, II, I, II, I, Select. If done right, the credits will appear instead of the title screen.