Your first job when you enter the zone is to take down Donna Troy. She's not
exceptionally tough, but it is a fairly long fight. AoEs and
crowd control are really helpful here to limit damage taken by the other mobs in
the room. You could take the smaller guys first, but I
found they were all easily defeated just off of my AoE damage.
In the next room, Starfire is much tougher. Again, the additional mobs in the room are easy to burn down so you can pretty much ignore them or if you lack AoE abilities, pull them first from the door. If you find yourself losing a lot of health when fighting her, hit shift or the R key when she starts spitting fire to avoid some of her damage. When she lets up the stream of fire, hit her with everything you have.
After releasing the prisoners and taking care of the two waves of science police that flood in, you now have to fight Cyborg. He has a few special moves that you'll want to avoid. He shoots pulses, pounds the ground, and charges a super punch. You can use your blocking skill to avoid most of the damage and break the stuns from these, then open up damage in between his moves to slowly take him out.
In the final room is Nightwing and Raven. Nightwing is actually easier than Starfire and Cyborg were. Avoid his spinning move and break his stun while working to kill him. Enter Raven's mind in order to finish up the fight!
Defeating Raven's individual spirits isn't all that hard, the hard part is keeping up your health. You don't regen in between the fights so if you used your soder cola during the previous fight, after you have defeated Raven's spirit, WAIT to interact (pressing E) with it. Your health won't go up but the timer on your soder cola will refresh. You can wait as long as you need to, the fight won't continue until you interact with the defeated spirit. Using this method, you can slowly get through the entire fight without dying as long as you have plenty of soder colas on hand.