How may Beowulf's defeat of Grendel be described as the defeat of the "dark side" of the warrior's life?
If Beowulf has a “dark side,” it likely is his ambition and love of glory, which is less a personal failing in him than a fundamental aspect of his society. Hrothgar is a good king, in that he has been successful in battle and rewards his men with treasure; nevertheless, he is humiliated by Grendel’s attacks on his hall, which he is powerless to stop. Twelve years Grendel ravages Heorat, during which time news of Hrothgar’s sorrow spreads through the world. Beowulf hears this story, and offers his help, mostly to increase his fame. When Beowulf does defeat Grendel (facing him unarmed, literally tearing him limb from limb), it is a great victory, of course, and earns Beowulf great glory. His subsequent defeat of Grendel’s mother, and of the dragon, only further increases his reputation.
To get back to the “dark side” part of the question, I don’t think Beowulf’s defeat of Grendel is representative of overcoming any sort of psychological shortcoming in his character. On the contrary, in a way Beowulf is a victim of his own success. Beowulf craves glory, because it is through achieving great deeds that one’s memory can endure. Yet the world Beowulf inhabits (an essentially pre-literate, and, in many ways, pre-Christian world) is full of dangers that can easily destroy not only him but his entire clan. There is a sense in the poem in which, despite his great deeds, Beowulf’s ability to protect the Geats cannot last. Once Beowulf is dead, his many enemies surely will attack. Beowulf’s “keenness” to win fame ultimately leads to not only his destruction, but (presumably) the destruction of his kingdom.
Any consideration of Beowulf's "dark side" must be found "between the lines" of the poem. It is never explicitly stated that Beowulf has any sort of psychological, moral, or spiritual dark side. He is presented as the quintessential Medieval hero: brave, loyal, and militarily powerful.
It might be possible to attribute Beowulf's braggadocio to an underlying insecurity about his fate in Denmark. Perhaps he is not quite as self-assured about his ability to defeat Grendel as he sounds; after all, no man has yet been able to even inflict the slightest injury on the monster.
When Unferth questions Beowulf's prowess regarding his earlier swimming match loss to Brecca, Beowulf snaps back with an insult of his own. Perhaps Beowulf isn't as confident as he seems about his prospects of defeating Grendel.
We should also consider the lengths to which Beowulf is willing to go to defeat Grendel. He actually lies in wait while Grendel attacks and kills his fellow Geat, presumably to lull Grendel into a false sense of security. It works, but Beowulf has allowed the death of his handpicked man. This might imply that Beowulf did not believe he was capable of defeating Grendel without the element of surprise on his side. This act is the only point at which Beowulf does something that the reader might question in terms of honor and loyalty. Nothing of this sort happens again.
In the epic poem, Beowulf, the hero (Beowulf) defeats Grendel. Grendel represents darkness and evil. Grendel has been banished into darkness given his ancestral link to Cain. Since his exile, Grendel has been required to live only in darkness and cannot enter into the light. As the foe of God, Grendel automatically becomes a foe of Beowulf.
The epic is written from a Christian perspective. This means that the story supports Christian theology and, therefore, the importance of good conquering evil.
Beowulf, the Christian hero, must defeat God's foe, Grendel. By conquering Grendel, Beowulf is able to show that God looks upon him with favor. Therefore, his defeat of Grendel depicts the crushing of the dark side of life. If Beowulf has a dark side, it is defeated by enacting revenge in the name of God upon the hell-monster.