People have their own definition of a “hero”, but Joseph Campbell created a step by step process a hero has to go through to be classified as a hero. Examples would be the “call of duty” and how quickly he answers to that call. Beowulf, when he heard about the torture in Denmark, made his way there to save their people. That act by itself would be classified as heroic to modern day people.
However, there are categories of Campbell's requirements that Beowulf does
not meet, such as “getting the lady” when he completes his task. Through the epic, Beowulf is rewarded with plenty of jewels, armor, and other precious gifts from Hrothgar, the king of Denmark. Furthermore, Beowulf was never “rewarded” with a female. Even when Beowulf fulfilled his duty of killing the monster that tortured them, Grendel, and went home, he never took a wife when he ruled his home. Modern day people would still consider Beowulf an amazing hero, even if he never “got the girl”.
An example of a heroic step that Beowulf met would be “meeting with a mentor”. Though he does not meet this requirement perfectly, Beowulf did get help; no matter how much he denied help throughout his battles. The help that he receives is advice from King Hrothgar, almost like fatherly advice or another elder male family figure. He also gets some help from Unferth, who gives Beowulf his sword named Hrunting to fight the creatures torturing Denmark. Though the sword does not work, it is still some form of help.
Beowulf may not meet all of the requirements that Joseph Campbell created for a hero, but modern day people would agree that Beowulf is a hero no matter what the “requirements” are. He worked hard to save the people of Denmark, and save his own people of Geatland as well. Beowulf saved lives, and that is enough to be classified as a hero.