Beowulf hears of Grendel and can't wait to fight him in person. Here Beowulf is asking permission from his bretwalda Hygelac to take 14 men to the land of the speardanes. His bretwalda tells him he is experienced enough to make this decision.
When Beowulf arrives he sees Hrothgar's Watchful warden and the Warden is startled since he thought Beowulf and his men were gonna invade them, but after things cleared the warden lead them in to the mead hall.
Here Beowulf fights Grendel and as Grendel tries to escape Beowulf rips his arm off and kills Grendel.
In this scene Grendel's mom kills Hrothgar's best mate Aeschere. Hrothgar blames Beowulf for this and sends him to kill Grendel's mother.
When Beowulf and his men as well as Hrothgar's men and Hrothgar himself arrive at the swamp, Beowulf gets ready to fight Grendel's mother at her lair with Unferth's family sword hrunting at his side.
After Beowulf looses Hrunting he sees a giants sword and fights Grendel's mom with it and defeats her and also chops her and her son's head off before coming back to the surface.