Wulfgar introduces Beowulf as a hero when he seeks an audience with the king, Hrothgar.
There is trouble in Herot. Beowulf has heard what the monster Grendel has done, and he has come to the rescue. Naturally the king’s man is suspicious, but Beowulf seems worthy, so he introduces him to the king.
“Men from afar have come hither over the ocean's paths—people of the Geats—and the most noble of their band is named Beowulf. … By their war-gear they appear worthy warriors, and their leader, a hero who led his band hither, is surely a valiant man.” (Ch. 5, enotes etext)
The fact that Beowulf is described as “worthy” and “valiant” underscores naming him a hero. In addition to being brave enough to fight a monster, he is willing to come all this way to put himself in the path of danger. He is a good leader, and he leads by example. He easily convinces them that he is a hero, and has ready answers for attempts to impeach his character or bravery. He is there, ready and willing to save the day. It is his persistence as well as his strength and honor that make him a hero.