User blog comment:Super Sub-Zero/Alternate Colors not appearing, and some are locked?/@comment-10558422-20140516163655

Palettes 7,8, 9 and 10 are unlockable in-game:
 * Color 7: Beat Story mode with that character
 * Color 8: Beat Arcade mode with that character
 * Color 9: Win with the character roughly 25 times in Versus (online and offline both count)
 * Color 10: Code is entered at the Controller Select screen in local versus as player 1.
 * for PC: idspispopd
 * for PS3: Down R1 Up L1 Square X
 * for 360: Down RB Up LB Y B

Palettes 14, 15, 16, 17 and 18 must be brought as DLC. It is called the 'Skullgirls: Color Palette Bundle'. I think it was free at one point, but now requires you to pay for it.

If you decide to buy the DLC though, you do not need to unlock the other colours as it unlocks them for you. It also unlocks all stages for you to play on instantly. :)