When you enter the room, half the raid goes to one side, and the other half stays. One room is deemed “live†(the one you enter) and the other room is deemed “undead†(the room on the right after the gate). Mobs that die on the live side respawn on the undead side. Ergo, you have to kill the mobs twice (their alive versions and their ghostly versions).
As the AoE healing Priest, I set up shop on the undead side with 4 other players. This resulted in 2 healers, a tank, and other DPS on the live side.
I suggest setting up Melee DPS on the Undead side and caster DPS on the live side.
You spend ~3 minutes killing the various waves coming in. After that time has passed, Gothik then teleports down to the live side (first room) and you can engage him. Then he switches to the other side and the undead group engages him. He keeps doing this back and forth. There are no waves for you to worry about at this point.
At 30%, the gates open and both groups can engage him without worry. He should go down without further difficulty.
Make sure the live side groups and the undead side groups are coordinating and communicating. Live side does not want to overwhelm the undead side!