To unlock every color in the game you have to play the Time Trial and Survival modes. Please note that these HAVE to be done in order. You con NOT skip to the challenges where the colors are. Also, you unlock these per color, not per Character. So you may complete these with for example: Ryu, and gain the colors of every fighter on the roster.

Color	How to unlock
Color 10	Survival Normal 16
Color 3	Time Attack Normal 1
Color 4	Survival Normal 1
Color 5	Time Attack Normal 6
Color 6	Survival Normal 6
Color 7	Time Attack Normal 11
Color 8	Survival Normal 11
Color 9	Time Attack Normal 16