DCUO Boss - Power Girl
Go into instances prepared! Always make sure you have a good supply of consumables, in this case have a stack of soder colas on hand. If you leave the instance prior to completing the mission, you'll have to start it over again.
To be able to do any damage to Powergirl at all, you have to turn the students in the ampatheater first. Powergirl lets off a big AOE stun followed by additional damage, so it is best to stay out of her way completely. Snatch the students while avoiding Powergirl until you have gotten enough to weaken her. At this time, Powergirl will become vulnerable to damage but she still fights back so be careful. You are locked into the room and you won't tick up in health while in battle, so be sure to have a full stack of soder colas on hand because you will need them. If you have ranged skills, use those. Parasite and his minions will do consistent damage to Powergirl so you really only need to not die while continuing to assist Parasite in the fight.