Beowulf, the protagonist in the epic poem Beowulf, can be defined as a epic hero in many different ways.
First, an epic hero is always introduced in media res, or in the middle of things. The fact that Beowulf is introduced long after Grendel's first attacks, after Hrothgar has closed Heorot, and after Hrothgar has given up hope for his kingdom.
Second, an epic hero is one who accepts a challenge that no one else will. Given that Beowulf enters Grendel's mother cavernous home alone, this shows that Beowulf is the only one who will accept the challenge. This shows Beowulf's possession of aristeia (nobility).
Third, Beowulf is a warrior, leader, and elevated speaker. It is the words of Beowulf which rally his band of men together to fight Grendel (and his death declaration at the end of the epic tale) which show him to be a polished speaker.
Fourth, Beowulf descends into Hell (or a Hell-like place) where he battles a foe of equal or greater strength (as seen with his fight with Grendel's mother).
Fifth, Beowulf's name is renowned. Once arriving upon Hrothgar's shores, his name alone allows his access to the king. The king knows of Beowulf and his epic challenges.
Sixth, Beowulf's foes (both Grendel and Grendel's mother) are "God/god despisers." Beowulf follows Christian ideology, and Grendel and his mother have been exiled from God's/god's light, making them "God/god haters."