Hold Left + B on Controller 1 and A on Controller 2 at the same time before the title screen appears (at the console power up/reset sequence or after the game over screen). Press Left or Right on Controller 1 to change the menu options. Press Up or Down to select the menu option. Press and hold Select to hide the menu.
When you get a game over and you're at the blue Afterburner screen, press A, A, A, A, B, Up, Up, Down, Down, Down, Down, Down and Down. If done right, you'll continue where you left off.
Once you've beat the game, press any button to continue to the Main Menu again. Now, when you start playing again, you'll be in a harder mode. The game won't tell you this, but you can see by harder enemies in the first stages who you'd normally come across only in later stages.
Before you start your game, hold A and B on controller 2 and then press START on controller 1.
At the Game Over screen, press A, B, and Select all at the same time.
Power the console on, wait for the 6 demo sequences to be played, then press A, A, A, A, B, Up, Up, Down, Down, Down, Down, Down, Down, Start.