Homer's Iliad is the most famous narrative of Achilles' deeds in the Trojan War. Achilles' wrath is the central theme of the poem. The Homeric epic only covers a few weeks of the war, and does not narrate Achilles' death.chilles was the son of the Nereid Thetis and Peleus, the king of the Myrmidons. Zeus and Poseidon had been rivals for the hand of Thetis until Prometheus, the fore-thinker, warned Zeus of a prophecy that Thetis would bear a son greater than his father.