When you beat ALL 5 Story missions in Mission mode using the indicated characters their alternative costume will become an available option. To select the alternate costume highlight the character at the selection screen and then press Triangle.
Unlock Amuro Ray Alternate Costume: Complete all five story missions in Mission mode with Amuro Ray.
Unlock Laura Rolla Alternate Costume: Complete ALL 5 Story missions in mission mode using Loran Cehack.
Unlock Zech Merquise Alternate Costume: Complete ALL 5 Story missions in mission mode using Milliardo Peacecraft.