"To free his weapon, and failed. The fight brought other monsters swimming to see her catch, a host of sea beasts who beat at his mail shirt, stabbing with tusks and teeth as they followed along. Then he realized, suddenly, that she'd brought him into someone's battle-hall, and there the water's heat could not hurt him, nor anything in the lake attack him through the building's high-arching roof. A brilliant light burned all around him, the lake itself like a fiery flame."
What details of the battle and its setting from Beowulf are characteristic of an epic?
Beowulf is an Anglo-Saxon poem which is considered an epic. The qualities of an epic include extraordinary heroism in the face of adversity, lofty language, and supernatural elements. The passage you cite contains all three of these elements.
Beowulf fights a battle, in the sea, against a host of sea monsters in addition to Grendel's mother. They are stabbing at him through his chain mail as he is being dragged through the water. We only have part of that battle here, but we know he "sank through the waves" for hours before he gets to Grendel's mother, and he is ultimately victorious in this battle. He fights alone against Grendel's mother and defeats her in her own lair.
The language in this passage is lofty. We do not have "a bunch" or "a lot" of monsters; we have a "host" of them. The kenning, "battle-hall," is a kind of lofty language, as well.
The most significant aspect of a heroic epic in this passage is the supernatural elements. First of all, all the action takes place at the bottom of the lake, a place where mere mortals could not possibly spend any significant time. Second, he manages to overcome a host of sea monsters in addition to the mother of a monster--all of whom could be considered supernatural because they are not of this world. Third, there is a battle-hall at the bottom of the ocean; if that were not enough, Beowulf can breath there. The lake (which of course is comprised of water) allows light and fire:
A brilliant light burned all around him, the lake itself like a fiery flame.
All of these elements demonstrate the epic qualities of Beowulf in general and this passage in particular.