At the Excelsior bridge menu, enter the following:

Level select:
Black, R, L, B, X, L, R, Y, White.

All ships:
Black, L, X, L, X, R, R, B, White.

Invincibility:
Black, L, B, L, R, Y, Y, B, White.

All medals and ranks:
Black, L, R, L, B, R, Y, L, White.

Kobayashi Maru difficulty setting:
Black, L, Y, L, L, X, Y, R, White.