Pause either R-Type game. Hold L2 and press Right, Up, Left, Right, Down, Left, Up, Right. Now press Triangle, Square, X, Circle, or R1 to get all weapons.
Highlight either R-Type or R-Type 2 at the main screen. Quickly press L2 10 times, R2 10 times. Start the game and pause. You should now see a 'stage select' option.
Pause either R-Type game. Hold L2 and press Right, Up, Right, Up, Down, Left, Down, Left. Now press Circle to increase or X to decrease the speed.
Thanks to Revolution readers Mark Northcott and El Dopa!