Achilles:

In most accounts of the Trojan battles, Achilles is the most prominent Greek warrior. In Shakespeare's account, Achilles has that reputation but performs no noteworthy deeds. He spends most of his time in his tent being amused by the impersonations of his aide Patroclus and accepting the adulation of the common soldiers for deeds he has performed in the past. In the minds of his military commanders, Achilles sets a dangerous precedent for the other soldiers who imitate him and take their ease, refusing to fight the Trojans. Achilles's arrogance has grown to such a degree that he refuses to answer even a summons from the Greek general Agamemnon. It is implied that the Trojan war drags on as a consequence of his inactivity.

When Hector issues his challenge to fight any Greek willing to do so, Achilles is the natural choice. But Ulysses, Nestor, Agamemnon, and others...