Anticipation Stage and "Fall" into the Other World
Achilleus gets in a fight with Agamemnon and refuses to fight alongside the other Achaians.
Even though it might be strange to describe the plot of the Iliad as one of "Voyage and Return," if you bear with us, we think you'll agree that it makes a bit of sense. First of all, you have to bear in mind that Homer's poem is a story about the anger of Achilleus. Because this anger has the effect of alienating Achilleus from other people, it makes sense to think about that departure from ordinary society as a sort of voyage, from which he must ultimately return. Achilleus's decision not to fight anymore on behalf of his fellow Achaians is the first step of his voyage; he then seals the deal by getting Zeus to favor the Trojans in battle.
Initial Fascination or Dream Stage
Just as Achilleus hoped, the Achaians start getting defeated in battle. After a particularly bad day of fighting leaves the Trojans encamped on the plain, they decide it is time for drastic action. Nestor suggests they ask Achilleus for help, and Agamemnon throws in an offer of extravagant gifts if he will come back to the fold. Achilleus flat out refuses.
In treating this as the "Initial Fascination or Dream Stage," we're following the interpretation of Achilleus offered by Diomedes at the end of Book 9. He says that Agamemnon should never have offered Achilleus all those gifts, because nothing would inflate Achilleus's ego more than to send them back. So long as the Achaians keep coming begging and he keeps playing hard to get, Achilleus is getting exactly what he wants.
When things get really bad for the Achaians, Patroklos begs Achilleus to let him lead the Myrmidons into battle. Achilleus agrees. Patroklos's counterattack is successful, until he himself goes down in battle at the hands of the Apollo-Euphorbos-Hektor tag-team.
This is where Achilleus's plan goes seriously wrong. Instead of leading to a situation where everybody realizes how much they need, love, and respect him, Achilleus's actions have led to the death of the one person he valued most: his best friend Patroklos.
Swearing to avenge Patroklos, Achilleus gets a new suit of armor crafted by the smith Hephaistos. Then he charges back into battle, and eventually kills Hektor. Even this, however, is not enough to assuage his grief.
Achilleus completes his departure from ordinary human society by repeatedly abusing Hektor's corpse and performing human sacrifice over the pyre of his friend Patroklos. His voyage into a world of his own making isn't looking so fun anymore.
Thrilling Escape and Return
The gods take pity on Hektor and tell Thetis to tell Achilleus to give the body back. They also tell Priam to go ask for it back. When he gets to Achilleus's place they experience a moment of shared humanity. They then negotiate a truce, so that the Trojans can bury Hektor in peace.
Okay, so it might not be your typical "thrilling escape," but Achilleus's action of sharing a meal with Priam—the father of his mortal enemy—definitely marks a return to ordinary human life after so long spent way out on the edge.
Ironically, this moment is overshadowed by the knowledge that Achilleus himself will die soon—meaning that he has rejoined humanity just before he is fated to leave it permanently.