There are several methods of unlocking additional colors for each character's outfits. You can get up to 4 extra colors (E, F, G and H) for each charcter's Normal and Another outfit. Select the character and outfit of your choice, then do one of the following:

Effect - Code
Extra Colors - Clear Story Mode
Extra Colors - Clear any Mission in Challenge Mode
Extra Colors - Clear Time Attack Mode
Extra Colors - Awarded every few stages in Quest Survival