I hope that I am correct in assuming that man vs nature and man vs the environment are the same thing.
In Beowulf, it is hard to know whether Grendel and his dam (mother) are considered people or deviations of nature, as they are usually referred to as monsters. However, there are at least two clear examples of this kind of conflict after Grendel's mother takes Hrothgar's most-loved "councillor and friend," Æschere, from the mead hall and kills him. In Chapter Twenty-one, Beowulf assures the Danish king that he will go after Hrothgar's lost man; as Hrothgar accompanies Beowulf, they find Æschere's head along the way, and the waters of the swamp are bloody.
In Chapter Twenty-two, Beowulf pursues Grendel's dam to an underground cavern, out of the water—a place like an open cave. Note the alliteration used to describe Grendel's mother; she is called...
That grim and greedy goblin...
When she realizes that a human has ventured into the "realm" that she has ruled for "a hundred winters," she tries to stab him and fails; then she tries to reach with her claws into his flesh, but his armor stops the creature both times. At this point, the monster decides to pull Beowulf underwater to her lair.
We see two examples of man vs the environment here: first, Beowulf must battle the water as first enters the "eddying floods." The translation notes that it is a long way to the cavern:
It took most of the day before he could reach the land at the bottom.
Once Grendel's dam realizes she cannot kill Beowulf in the cavern, she pulls him into the body of water again, where he is attacked by violent monsters and dangerous "sea-beasts"—forms of nature:
Though his valor held, he struggled in vain to wield weapons against the terrifying monsters that set upon him while he swam. Many sea-beasts tried to tear his mail with fierce tusks when they swarmed upon this stranger.
These are two examples of man vs the environment in the epic poem, Beowulf.