Beowulf is clearly a courageous man, and is motivated by a desire to prove his valor to others, through both accomplishing brave feats and then boasting of them to others. Early audiences would not necessarily have found this to be vain, especially since the poet often has Beowulf give credit to God for his bravery and his skills in combat. He arrives at Hrothgar's hall full of stories about his valor and his prowess in battle, and, as the reader eventually finds out, he can back them up. He is not necessarily motivated by altruism in his mission to kill Grendel, but rather by a desire to prove himself and enhance his reputation, a perfectly valid motive in his day:
Hail, Hrothgar! My followers and I are Hygelac's kinsmen. I have gained much fame in my youth! ...[T]he best of my people,...know full well the strength of my might. They themselves were witnesses when I came from battle, flecked with my foes' blood; there I bound five beasts and bested the brood of giants. I slew beasts by night on the waves, avenging at my own peril the Geats, whose woe they sought—I crushed these grim ones. Grendel, this cruel monster, will now be mine to best in single battle!
He demonstrates his bravery through three deeds in the poem. In the first, as mentioned above, he saves Hrothgar and Heorot by killing Grendel in hand-to-hand combat. He then dives to the underwater lair of Grendel's mother and kills and decapitates her. Then, much later, as an old man, and King of the Geats, he ends his life in a mortal struggle with a dragon that was terrorizing his people, with the help of the noble warrior Wiglaf. Throughout his life, then, Beowulf demonstrates his courage by taking on and destroying evil monsters, and protecting those people who are weaker than him.