Beowulf is an epic Anglo-Saxon poem, and the man for which it is named is an epic hero. This passage is found toward the end of the poem as well as the end of Beowulf's life. He is fighting alone against the dragon; one lone follower, Wiglaf, is nearby.
And for the first time in his life that famous prince fought with fate against him, with glory denied him. He knew it, but he raised his sword and struck at the dragon's scaly hide.
This passage reveals everything we need to know about the nature of an epic hero.
First, Beowulf is called a "famous prince," and one of the characteristics of an epic hero is fame and glory. Second, he recognizes that fate is in control of his destiny, an important element in an epic hero's story. He will fight until fate keeps him from fighting the next battle. Third, he fights for glory as well as to protect his people from a dragon. Glory is all, but this time it will be denied him. Fourth, Beowulf knows he is defeated but fights with valor anyway, a sure indication that Beowulf is an epic hero. Fifth, with his figurative last breath, he raises his sword and strikes the enemy. That is the goal of every epic hero--to strike a death-blow at the enemy, no matter what it costs him.
In every way, then, this passage presents the picture of an epic hero, and his name is Beowulf.