To unlock the costume colors for a certain character you must rank up that character to Mentor, from there you will unlock a new color until you reach Vindicator, 10 colors total for each character including default color.

Color	How to unlock
Color 1	Reach the rank of Mentor.
Color 2	Reach the rank of Master.
Color 3	Reach the rank of Rogue.
Color 4	Reach the rank of Brawler.
Color 5	Reach the rank of Marauder.
Color 6	Reach the rank of Berserker.
Color 7	Reach the rank of Warrior.
Color 8	Reach the rank of Avenger.
Color 9	Reach the rank of Vindicator.