Lady Deathstrike is the second "boss" that you would normally fight, and she has a grudge against Wolverine. However, if you are using the "Brotherhood of Evil" layout (Magneto, Scarlet Witch, Juggernaut, and Toad), when the chatting sequence comes into effect, pay attention. The option will come up to pay her off for just 1000 tech bits, instead of fighting her. It's an easy way to avoid the hassle of this particular boss.
Type in this cheat while playing normally, use the control pad, not the control stick, for the directions.
Put in the first code at the Danger Room menu
Put in the second one during the Team Select screen at an Xtraction point.