Once you hold a Yggdrasil, you have the ability to kill Grendel. You must find him, which should be easy since he has been harassing you all this time. You could hang out in Heorot Hall and wait for him. He makes frequent trips there each night. Once you encounter him, grapple him until you kill him. You gain the status of Super-Hero Grendel Slayer and you have won Grendel's Cave. At this point you have the option of trying to kill Grendel's Mother, who will appear soon after you kill her son, and then, after you do away with her, killing the Dragon. This is the triple crown of Grendel's Cave and only a few have completed the task.