In what ways does the conflict between Achilles and Agamemnon prevent the Greeks from achieving their ultimate goals, and how could this have been resolved or avoided?

Achilles is in a state of high dudgeon. He feels that his honor has been impugned by Agamemnon, king of Mycenae. Agamemnon has appropriated Briseis, Achilles's comely concubine, in compensation for the loss of his own sex slave Chryseis. Although, to be fair to Agamemnon, he didn't have much choice in the matter. He had to return Chryseis to her father to remove a deadly plague unleashed upon the Achaeans by the god Apollo.
Achilles is absolutely furious. He storms off and retreats to his tent where he sulks and simmers with rage. Agamemnon does make strenuous efforts to resolve the conflict; he brings lavish gifts to Achilles; he even offers him his daughter's hand in marriage (not Iphigenia, though, as she's already been sacrificed). But Achilles is implacable; he behaves like a sulky adolescent hiding away in his bedroom. He won't return to the fray until after the death of his bosom buddy Patroclus.
Under the circumstances, it's difficult to see what else Agamemnon could do to placate Achilles. After all, he's the king, and as such has authority over Achilles. But Achilles is half-god, half-man, so thinks he's on a higher level than pure mortals such as Agamemnon. His pride is so great that there's no point in trying to reason with him.
That said, Agamemnon must have known what Achilles was like. He really shouldn't have taken Briseis of the lovely cheeks away from him; he was just asking for trouble. And Agamemnon does realize this himself, which is why he eventually apologizes to Achilles for his rashness. But Achilles, of course, won't accept his apology, and the Achaeans continue to falter on the battlefield without their greatest warrior.