In Beowulf, describe the setting where the fight of Beowulf and Grendel's mother takes place.
Little is actually written in terms of a full description of the location of this momentous battle. It happens in the depths of the lake that Beowulf dives into and then in the vault that Grendel's mother takes him to. It is clear that both the depths of the lake and the vault are described as very dangerous places that threaten Beowulf's life. Grendel's mother is not the only beast, and as she clutches Beowulf and takes him with her to her underground lair, other creatures try and attack Beowulf:
...a bewildering horde
came at him from the depths, droves of sea-beasts
who attacked with tusks and tore at his chain-mail
in a ghastly onslaught.
The few descriptions that the reader is given of the location of this battle are variously a "hellish turn-hole" and a "vault." It is only after Beowulf has slain Grendel's mother that "The place brightened" and he is able to find his way to Grendel's corpse to behead it, but still little description is given of Grendel's mother's vault. Throughout the main focus is on the titanic clash between Beowulf and Grendel's mother and the allegorical nature of this battle as good meets evil and good finally vanquishes evil.
Several key attributes define this location.
First of all, it is far from human habitation.
Second, it is on the monster's home ground. Remember that Grendel had intruded into where the men were sleeping. In that attack, a monster intruded into the human realm. In this attack, Beowulf, a human, intrudes into the monster's home realm. So, it is a reversal.
Third, it is at the bottom of a lake. This is both a sign of Beowulf's heroic prowess--who but a great hero could hold his breath this long and still fight--and symbolizes the fact that this is Grendel's mother's court. It is a kind of underworld.
Fourth, it is a dark cave full of monsters and other animals. However, the cave is also the site of other battles and trophies: there is a giant sword on the wall (that Beowulf will soon use).