Hyper Speed:
Press and Hold X, L1, R1 and Select on main menu.

Mission Simulator:
Unlock all five endings with a pilot. You can play any mission with any airplane on any difficulty setting with the Mission

Simulator.Control replay: 
Press Square, Triangle, O, X, L1 or R1 during the replay to change camera angles. Press L2 to add a filter, as if the view were through sunglasses. Press R2 to add motion blurring.

Japanese Intro Movie
Complete the game on the Hard difficulty.

Music Player
Complete the game on the Easy difficulty.

Unlock O.S.L. (Orbital Satellite Laser)
Earn straight A's for all 36 missions in the Mission Simulator on Hard.

NOTE: The O.S.L. is not availible for use in missions: 16,18,32, and 33.

Unlock U14054 Aurora
Earn straight A's for all 36 missions in the Mission Simulator on a difficulty higher than easy.

Unlock X-49 Night Raven
Earn straight A's in all 36 missions in the Mission Simulator on a difficulty higher than Normal.

Unlock the XR-900 Geopelia
Defeat the hidden, 36th, mission in the Mission Simulator with an A.

Mission simulator
Unlock all five endings with a pilot. You can play any mission with any airplane on any difficulty setting with the Mission simulator.

Replay camera control
Press Square, Triangle, Circle, X, L1 or R1 during the replay to change camera angles. Press L2 or R2 to add different filters.

Watch Original Intro Movie
This combination lets you watch the original japanese intro movie for this game. The movie is much cooler than the one you usually see, and hints at the elaborate storyline that was removed from the game when it was brought to the US.
Well enough about that, here is how you get to see the movie:
To view the movie, go to the Title screen where it says "Press Start" and hold down L1, L2, R1, R2, Then press start and select at the same time. The movie will then play.