Beowulf is constructed with many complicated and intricate layers that are fascinating to explore. In these layers, one can find that this epic is quite different than other narratives, and as such I would hesitate to apply the label of tragic hero to Beowulf because he and the epic are something unique. Joyce Lionaron has tackled this dimension through a term coined by Bakhtin, chronotope. This singular term combines aspects of time and space. To best describe this element of the epic, here is a quotation from The Medieval Dragon: The Nature of the Beast in Germanic Literature:

Time in Beowulf is dominated by a nostalgic, almost thematic sense of the past. All of the poem's events take place in geardagum, "in days of yore," and can be known only as a result of a present questioning of the past: the narrator's words for this is gefrunon, "learned, heard of," which in its root sense means "asked and received answers" or "learned by asking." In looking at precisely how and by whom the past is questioned in Beowulf, however, one quickly discovers that there is more than one 'past' being questioned by more than one 'present' within the poem.

To break this down, the author of Beowulf is a Christian Anglo-Saxon looking back at Germanic tales and pagan life. Furthermore, the author creates layers of a mythological past (seen with tales of Sigmund), historical past (constant mention of blood feuds), Christian myth (mentions of Cain and Abel), and heroic action (fighting with Grendel, Grendel's mother, and the dragon). However, these layers can be seen as fluid as well. In particular, a lot of them can be seen to impact Beowulf.

The first half of the epic has the rise of Beowulf as a warrior and hero. He drives away Grendel and slays Grendel's mother, who plagued the Danes. Humanity has prevailed and happiness can return. However, reality is crueler. In the background, the blood feuds sung are still happening and even when the monsters are gone humans will still be plagued by themselves. This is where the second part of the epic takes off. Beowulf has become king of Geatland and has protected the land for over 50 years, but he is old now and mortality is in front of him.

Now, when we look at the typical characterization of a tragic hero, this is different from something being tragic. Usually the definition of a tragic hero entails a fatal flaw, which does present an interesting argument for Beowulf. Beowulf embodies the aspirations and traits of a Geat. He does not fear death, he gives gifts to his subjects, and he lives with honor. This is in contrast with the dragon. The dragon hordes his treasure and wreaks havoc on the land and the people. Another foil to Beowulf is his men. Only Wiglaf is brave enough to fight with Beowulf. Furthermore, when the fighting is over, Wiglaf directly reprimands the subjects who failed to come to Beowulf's aid:

Wiglaf, son of Weohstan, spoke
Disdainfully and in disappointment:
“Anyone ready to admit the truth
Will surely realize the lord of men
Who showered you with gifts and gave you the armor
You are standing in—when he would distribute
Helmets and mail-shirts to men on the mead-benches,
A prince treating his thanes in hall
To the best he could find, far or near. (2862–2870)

Given this and the complexity of the epic, it would be slightly simplistic to see Beowulf as fighting only for himself. Furthermore, as stated earlier, the author is looking back and exploring themes in the epic. He can be seen to both respect and lament the positions of his predecessors. In this way, the idea of a tragic flaw or tragic failing can be applied to the culture of the pagans and Beowulf, who embodies those beliefs. But with everything said, there is a lot of ways this work can be examined, and a lot of arguments can be made. In particular, the themes of mortality are important. Beowulf's death is a vain one because invaders will attack Geatland after their strong king has died. So, I leave off with a few questions to ponder: Why does Beowulf's death matter? Or does it not matter? How is mortality different when viewed through a Christian lens and a pagan one?

One normally associates Beowulf (from the epic Beowulf) as an epic hero, not a tragic one. That said, when applying the characteristics of a tragic hero to Beowulf, one could support that he falls into this category as well.

In regards to his fight with the dragon, Beowulf desires to fight the beast alone. This could illustrate his hamartia (or tragic flaw) as one which is prideful and narcissistic). This said, his solo fight with the dragon could illustrate that he believes far too much in his own power that he cannot be beaten. This could show his tragic side.

That said, if one supports the idea that Beowulf fought the dragon for his people, this would show him aligning with the epic hero. One of the characteristics of the epic hero is to help others. By fighting and defeating the dragon, Beowulf insures that it will no longer torment his people.

Therefore, he would only be classified as a tragic hero if his hamartia was the reason he fought the dragon. Fighting for his people would not make him a tragic hero at all.