Nine lives & all weapons:
Press Start, then at the title screen, hold A + Down and press Start.
Invincibility:
Press Up, Right, Down, Left, Up, Up, Right, Down, Left, Up, Up, Right, Down, Left, Up, Up, Right, Down, Left, Up at the copyright screen. Then press Start.
Level skip:
Press Up, A, B on controller two.
The Genie has more
Captain Skyhawk Cheats at CheatingDome.com.