Follow these easy steps to unlock a character's color:

1. Go into Arcade mode (Battle -> Arcade)
2. Enter Battle Settings by pressing RB/R1 or whatever button you assigned to it
3. Set difficulty to 'Very Easy' and damage to 'Highest'
4. Close and choose any two characters you want to unlock colors for and any stone. If you're in doubt, I suggest you to always pick Soul Stone in case the AI suddenly decides to retaliate, as it can give you life back or revive a dead teammates.
5. Once you're in a match, just do magic series into magic series repeatedly to kill them. If you don't know what a magic series is, it's a universal sequence of buttons that combo for every character in the game. The basic magic series can go as following:
LP LK HP HK cr.HP (launch) LP LK HP HK (ground bounce) cr.LK HP cr.HP (launch) LP LK HP HK
This sequence should kill almost every character. There might be some slight variations depending on the character you're playing or your position on the screen but you can just chase them down and do the series again.
If you're really lazy you can also use auto combos and mash LP repeatedly until they die.
6. Once you get into Battle 6, wait for 'Fight!' to appear on the screen, then press Start and exit to Main Menu

Once you get back to the main menu, the game will tell you that color 3 is unlocked, or if color 3 was already unlocked, color 4.
And that's it. You don't need to finish Arcade mode, just to finish a total of 5 fights for every color you want to unlock.
Note that only the total number of matches count. If you already played 7 matches with a character you'll only need 3 more to unlock color 4.
If you don't like grinding Arcade mode you can also unlock the colors by playing a certain number of matches online.

Note: The colors will be unlocked for all costumes you own for that character. You don't need to do this again if you bought an alternative outfit!

Have fun rocking your pink Ultron or golden Arthur!