Stand away from the room she's in, on the left wall of the room there's a visceroid. Shoot it with the pistol until it's dead. On the right wall there's two initiates. Shoot them too. Then, put C4 all over the floor. Watch the cutscene. After it's over, take a few steps back and head down. Time it for about when the Black hands will step on them, then detonate. Get out the rocket launcher and get to the bottom floor. Health and armor spawn there. Kill her from here, you may have to kill some black hands though too.