What evidence is there of Beowulf keeping his promises?
When Beowulf comes to Heorot, he informs Hrothgar that he has heard of the destruction Grendel has caused and he promises to kill the monster. He adds that since Grendel does not use weapons, he will fight the monster alone with no weapons:
. . . I scorn to bear sword or broad shield, yellow wood, to the battle, but with my grasp I shall grapple with this enemy and fight for life, foe against foe.
Beowulf is also criticized by Unferth who says he lost the swimming contest with Brecca. Unferth is skeptical and thinks that tales of Beowulf's skills are exaggerated. However, Beowulf claims that he fought nine sea monsters during the race and that such a feat has never been equaled. In killing Grendel, Beowulf promises to prove himself and that tales of his accomplishments are true.
Beowulf does fight Grendel alone with no weapons. He manages to tear the monster's arm off: Grendel's "shoulder was exposed, his sinews sprang apart, his bone-locks broke." Grendel runs off to die and Beowulf has kept his promise.
After Grendel's mother attacks, Beowulf promises to track her down and kill her. "I promise you this: she will not be lost under cover, not in the earth's bosom nor in the mountain woods nor at the bottom of the sea, go where she will." He finds her in a lake and fights her to the death. He fights her a lone once again and manages to kill her using a sword he finds in the lake-cave. Once again, he has kept his promise.