Note: Shoutout to Mr. Wall for this simplified breakdown of Aristotle's elements of tragedy! Also, I'm using the Greek spellings of the characters' names, except for Achilles because everyone kinda knows him already as Achilles.

The Iliad fits the key requirements of a tragedy: it depicts an action (the Trojan War), includes artistic embellishment (epic form), evokes pity, fear, and catharsis, features a tragic hero with a tragic flaw, and has a complex plot. The issue of whether or not it's a tragedy in itself is not what's in question here; but rather, who is the tragic hero?

If you were to argue that Homer's Iliad is indeed representative of Aristotle's idea of a tragedy, the obvious choice for the tragic hero is Hektor. He's much more humanized than Achilles: he was generally anti-war, fought to protect his city despite being told he would die, and was a loyal husband and a good son. His tragic flaw can either be his loyalty to Troy, or his refusal to accept his fate: he was told he would die in the war, but he fought to defend his city, widowing his wife and leaving his son fatherless. But if he is our tragic hero, then what is his great tragedy besides his own death? If the tragedy is his death, where is there room for him to reflect and recognize his flaws? The tragedy would not fall upon him, but on his wife, for she's just lost her husband and must be the sole provider for their son. Hektor hits almost all the points of the tragic hero; objectively, he's the most moral character in The Iliad—how could anyone sympathize with the brutal Achilles? But every story has two sides, and for the sake of debate, maybe it's Achilles who's the tragic hero of the Achaeans. 

If we are to argue that Achilles is the tragic hero, not necessarily just for his own side of the war but for the entire Iliad, the number one issue that prevents him from immediately being interpreted as such is the fact that there is little room for pity; he's literally a war criminal. However, Achilles's pride, ambition, and devotion is something most can relate to. He's determined to fulfill the prophecy he heard as a child and be the great demigod warrior he was raised to be, to defend his country, defend his people, and be damn good at it. However, the audience only feels true pity for Achilles when he suffers his great tragedy: losing his beloved Patroklos. To take it back to Mr. Wall's class, where I first learned about this structure, in The Crucible, there isn’t a whole lot of sympathy for the tragic hero, John Proctor, either until his life starts going downhill. If we are to identify our own ambition in Achilles—translated for a modern day, of course—then we realize the pitfalls of our own determination: if we are too ambitious in achieving our goals, too cunning and driven, will we destroy ourselves and any sense of morality we once had?

While Achilles may not be a hero to us—especially through a modern lens, in a time when raiding and pillaging innocent villages is pretty severely frowned upon—he was to the Achaeans. He was their way to win the war and go home after nine long years in Troy. There is glory and honor associated with his name: he is a demigod, a prince, and a commander of the Greeks, he's renowned, prosperous, and purposefully morally ambiguous. Hopefully you see him as straight-out evil on account of all the war crimes, but at the end of the day, he's fighting for what he believes is right and for his country. There are many situations where we should NOT apply that sort of logic, particularly those in which the cause that said passionate person is fighting for is inherently wrong, i.e. beliefs that go against who a person is at their core, or things they cannot change about themselves. Achilles's mission isn't inherently wrong: he's just helping his buddy get his wife back after she was kidnapped. The way he went about accomplishing it certainly was, but that's not the point. Not to sound like an elderly lady or anything, but he's from a different time. 

It's not a tragedy without an essential question, and when we look to Achilles, there are two main moral questions: If my honor was threatened, in a time where honor was all someone had, would I defend it and doom others? A more modern translation of this problem (putting the honor portion of it aside) is the trolley problem: Would you save one person you know and kill several that you don't? The second question takes us back a little before the plot of the actual Iliad, but is the essential question that drives Achilles to this level of insanity: Would I choose greatness, fame, and glory, but die young, or settle for stability and a long, quiet life? Achilles was raised as a powerful demigod; from the time he was young, he was told he was destined for greatness. How could he disappoint the gods and not choose glory? Thus is Achilles's hamartia: hubris, or pride, the most common fatal flaw in Greek mythology and literature—besides Zeus's lust, of course. 

To put Achilles's actions into perspective, I'll boil down the situation: In fighting for what he believes is the right thing to do, whether it be objectively wrong or not, he agrees to let Patroklos dress up in his armor and pretend to be him so that Patroklos can lead the Achaeans and put an end to the senseless slaughter of his army. Achilles wants to win the war, truly, but his pride and stubbornness get in the way of his moral capacity to do so. (Read: incredibly morally ambiguous. This guy's moral compass is a Roulette wheel.) In agreeing to what he sees as a solution, having a highly skilled warrior pose as him in a way that would not arouse suspicion, the Greeks will match the Trojans once more. Of course, this leads to the death of Patroklos, and Achilles loses the person dearest to him and, as a result, his own life. The art of the fatal flaw is that it is something that could happen to anyone, a simple error in judgment. Achilles believed he was fixing his errors by taking the easy way out, and it made things much worse for him instead. 

When Achilles's good fortune reverses, when Patroklos is killed despite being such a skilled warrior and surviving nine years of the Trojan War (a surprising but necessary outcome as a consequence of Achilles's pride, as Aristotle puts it), Achilles realizes that his pride was the reason his beloved Patroklos died. Thus, he proclaims vengeance on Hektor, the one who had killed Patroklos, despite the fact that it was prophesied that once Hektor died, Achilles would too. In his distress, Achilles defaces Hektor's corpse in the most demeaning and psychotic way possible, exhibiting his development after his reversal of fortune and great tragedy, thus warning the audience to keep their flaws in check and to do the right thing rather than the easy thing, lest they lose the one they love the most and all sense of themselves. 

Of course, Homer may have intended the Iliad to be an entertaining recount of events, though very embellished for the sake of entertainment, and not a tragedy at all. If you google "the iliad tragic hero", the top choice is always Hektor. But there are two sides to every story, and in my opinion, both sides can have their tragic hero; that is, of course, if both sides aren't fighting for something objectively and morally wrong.