Keio's Flying Squadron
Note: This game is also titled Keio's Flying Machine. 

Super Catch mini-game:
Press Left(2), Right(2), Down, Up, Down, Up at the title screen. 

Level select:
Press Right, Left, Right, Left, Down, Up, Down, Up, Right(4) at the title screen. A level number will appear at the top of the screen to confirm correct code entry. Use the D-pad to select a new starting level. 

Power-up Rami:
The weakest character is Rami. Hold L + R for approximately five seconds to power her up.