For all DLC characters (Cyclops, Hawkeye, Hulk, Nightcrawler, Magneto, Dr. Doom, Sabretooth, Venom), you need 250 total kills to unlock all 4 outfits.
Outfit 2 - 30 kills
Outfit 3 - 175 kills
Outfit 4 - 250 kills
You can use the Kurse simulation mission to grind this as enemies infinitely spawn. You do not need to complete the mission for kills to count.