There are several ways in which Beowulf is a paradigm of the heroic epic. One way is that Beowulf feels the call to adventure and leaves his land to aid Hrothgar, whose domain has been menaced by Grendel. The call to action is an element of the heroic epic, and...
Beowulf is the archetypal hero who, without hesitation, heeds the call to take to the seas, though the journey is dangerous. In Book V, Beowulf says, "From feelings least selfish/I am able to render counsel to Hrothgar." He states that his motivations to help Hrothgar are entirely selfless. This element of the epic would probably most likely be expressed through the consciousness of the character, as the hero heeds the call to go abroad and court danger.
The second element that makes Beowulf a paradigm of the heroic epic is the ordeal in which Beowulf takes on Grendel and later Grendel's mother. The ordeal proves the hero's might and is most vital in an epic. In slaughtering the monster Grendel, Beowulf clearly has God on his side. Beowulf's victory is told in the following way in Book VIII:
At last for the Danemen,
When the slaughter was over, their wish was accomplished.
The comer-from-far-land had cleansed then of evil,
Wise and valiant, the war-hall of Hrothgar,
Saved it from violence.
Beowulf's slaying of Grendel is not portrayed as causing blood but instead as a kind of purification, a cleansing of Hrothgar's hall that Grendel had besmirched by spilling the Danemen's blood. Beowulf is clearly on the side of good, and evil has been vanquished. This element of an epic is likely best told through poetic or narrative consciousness.
Finally, Beowulf, at the end of his days, has a hero's funeral and an ending befitting a hero. His people construct a funeral pyre for him:
Then wailing war-heroes their world-famous chieftain,
Their liegelord beloved, laid in the middle.
Soldiers began then to make on the barrow
The largest of dead-fires:
When Beowulf dies, his people tell of his greatness, adding to his lore and ensuring his memory will live on. This part of the epic is best told through narrative consciousness, as the hero has died and cannot tell of his death in his own words. There are other elements of the epic as well, such as Beowulf's crossing into the land of the Danes or Beowulf's reward of treasure, that you might also write about as elements of the heroic epic.