Legendary heroes of old, like Beowulf, have a lot in common with modern day heroes. In fact, in my media studies class, I show students exactly how much Beowulf has contributed to modern day heroes. Your question could have asked about any number of currently popular comic book heroes, and their characteristics are strikingly similar to Beowulf's characteristics.
One key feature to a legendary hero is that the hero has to look like a hero. Big, strong, young, and handsome. Think Captain America or Thor for this one. A legendary hero has to look the part. They have to look like a warrior. This absolutely applies to Beowulf. Near the beginning of the poem, Beowulf is on his way to see Hrothgar. A guard stops him and demands to know what Beowulf's purpose is. The guard gives a brief description of what Beowulf looks like.
Nor have I seen
A mightier man-at-arms on this earth
Than the one standing here: unless I am mistaken,
He is truly noble. This is no mere
Hanger-on in a hero’s armour.
That clearly shows Beowulf as looking the part of a mighty warrior. Beowulf is also very strong as evidenced by the following quote.
Who valuable gift-gems of the Geatmen carried
As peace-offering thither, that he thirty men’s grapple
Has in his hand, the hero-in-battle.
Plus, don't forget that Beowulf literally tore the arms off of Grendel.
Another character trait of legendary heroes is that they are brave. Beowulf is clearly a very brave warrior. He chooses to fight Grendel. It's not like he is doing it out of self-defense. Grendel is not a small fight either. Not a single warrior has been able to defeat him yet. Plus, Grendel is scary. He's said to be demon possessed, and he eats humans.
Other traits of legendary heroes are that they are victorious while still being humble. That's true of Beowulf. He defeats both Grendel and Grendel's mom. At one point, as a reward, Beowulf is offered the Danish throne and immense riches. Essentially, Beowulf is offered fame and fortune, but he turns in all down and returns home the same way that he left.
I think the last defining characteristic of a truly legendary hero is that a legendary hero ultimately dies in battle. Beowulf does defeat Grendel's mother, but he is mortally wounded in the fight. He dies as a legendary hero. This is probably single greatest difference between Beowulf and modern day comic book heroes. They hardly ever die.
Beowulf is a legendary hero is driven by affection and duty, not personal glory. He seems obvious to fear. Personal glory is not meaningless to Beowulf. He tells Hrothgar that the best thing men can do is to lay up fame before death (lines 1386-89). He willingly accepts treasure but just as willingly passes it on to others. Nevertheless, duty, sympathy and generosity are his primary motivations. What may endear Beowulf to his audience even more is that, despite his great strength, he is a man with limitations. This helps the audience identify with him because in each of his fights he is seriously challenged and clearly sees himself as relying on the help of God. Thus, even though some of his feats seem clearly supernatural, he is characterized as a mortal man who overcomes many challenges in his life.