Compare and contrast the two principal warriors in Homer’s Iliad, Achilles and Hector, in terms of their actions and their character.

Both of these great warriors subscribe to a heroic code in which honor is everything. There are countless different ways to achieve honor in their respective societies, but primarily it is achieved through feats of physical courage on the field of battle; and it is here, in the theater of conflict, that the actions and characters of Achilles and Hector can most usefully be assessed.
Though Achilles is undoubtedly the greatest of the Achaean warriors, he fights primarily for himself and his own glory. Even as his comrades are being comprehensively slaughtered in battle, he still won't lift a finger a help them. He remains sulking in his tent, still brooding over the commandeering of his sex-slave by Agamemnon.
Eventually, Achilles does venture forth to do battle with the Trojans; but even then it's for purely personal reasons. Just as injured pride keeps Achilles sulking in his tent, so too does it cause him to emerge. To Achilles, the slaying of Patroclus at the hands of Hector, breaker of horses, is nothing more than a personal insult, one that must be avenged with the utmost brutality.
Achilles has an almost insatiable lust for blood. He actually enjoys hacking his way through the Trojan ranks, heedless of the consequences to himself or others. There's a fine line between bravery and recklessness, and Achilles crosses that line several times. Even when he finally kills Hector, his lust for savage vengeance still remains unsatisfied. His completely gratuitous degradation of Hector's corpse is further proof of his almost insane lust for violence. One can hardly imagine Hector doing the same thing to Achilles, or anyone else for that matter.
The reason for this is that Hector fights because he has to, not because he wants to. His honor is at stake, no less than that of Achilles, but unlike the Achaeans' finest, he's acutely aware too of the honor of his family and of his city. He's not just fighting for himself as Achilles does; he's fighting for a higher cause.
Hector's conduct on the battlefield couldn't be more different, either. He won't hesitate to beat a tactical retreat to minimize loss of life among his men. Though every bit as courageous as Achilles, Hector doesn't act recklessly; there's simply too much at stake. He can't afford to be gung-ho about a war whose outcome will mean the difference between life and death both for himself and his beloved city.