The Griever

Overview

The Griever first appears as you enter the Hollow area, a former human subway station, and then later at the end of the dungeon. She likes to spawn hordes of locust enemies during the battle. 
 

First Encounter (spoilers)

Right as you enter the dungeon, you will come face-to-face with the Griever. Using the Redemption minigun that a few angels left behind, you will be able to scare her off.  Be sure to dodge her laser beam, it's quite powerful. 
 

Final Encounter (spoilers)

At the end of the dungeon, you will face the Griever once more. This is battle is far trickier than the earlier. The main weapon used in this battle will be the Tremor Gauntlet. You must clear out all the blue crystals in the way of the train car, while dodging her laser beam. The catch is, if her laser beam comes in contact with the blue crystals, they will become unbreakable for a certain amount of time. Also, if you try to just run up to her, she will push you back every time.
 
Once you have broken all the blue crystals in the way of the train car, you must grab the train car, and punch it into the Griever. Every time this is done, she is stunned, unable to push you back, and so becomes vulnerable to your punches with the Tremor Gauntlets. Be careful, she gets up rather quickly. Once she gets up, she will emit a horde of small bat-like creatures. Dispose of these guys quickly, because she will start causing rocks to fall where you're standing. Evade this enough and repeat the steps with the train car.  Once she's down for the count, a cutscene will start showing War ripping out her heart.