Enter and kill the two Skaarj inside. Pupae will begin spawning all over the room, so find some high ground, possible access the upper level through one of the lifts along the outer edge of the room.
When all of the Pupae are dead it’s show-time! The Skaarj Queen will appear in the centre of the room.
Fighting the Queen is difficult, notice that before she attacks, she rears and screams. Blast her before she launches projectiles at you, and then quickly circle her to avoid her attack. Keep up a steady stream of fire. Use the upper level - your Eightball Gun will lock onto her quite well from a distance.