In Beowulf, how do Beowulf's three major battles show his courage?
At the start of the poem, Beowulf is already known for his superhuman abilities and his battles with monsters that no one else can kill. Grendel, his first foe in the poem, has been terrorizing Hrothgar's mead hall for twelve years; all of Hrothgar's warriors and any other visiting heroes have been unable to fight or even harm Grendel. Beowulf takes on Grendel alone and without weapons; he trusts in his physical abilities, and he alone is able to kill Grendel by tearing off his arm. In his battle against Grendel's mother, Beowulf again fights alone; because of his past heroics, he is able to hold his breath and kill her, although the sword he brings is useless. Beowulf refuses help not because he is vain, but because he knows that companions would die, and he wishes to avoid more needless deaths.
"Earls in armor, which of us two may better
Bear his disaster, when the battle is over.
'Tis no matter of yours, and man cannot do it,
But me and me only, to measure his strength with
The monster of malice, might-deeds to 'complish.
I with prowess shall gain the gold, or the battle,
Direful death-woe will drag off your ruler!"
(Hall, Beowulf, gutenberg.org)
In his final battle against the dragon, Beowulf again attempts to fight alone, because he knows that the dragon will be too powerful for others. Although his strength and sword fail him, Beowulf is assisted by Wiglaf, who is himself the rightful heir to Beowulf's legacy. Wiglaf remains while all others flee; he is concerned both for Beowulf's life and for that of his people if Beowulf should fail. Beowulf, knowing that he is near death, accepts Wiglaf's help to kill the dragon; if he had died without killing the dragon, his people would suffer. In this battle, Beowulf puts his ego aside and is victorious because of his love of country and people, not because he wants to have one final victory for himself.