Metamorphoses Book 12: The Death of Achilles
Ten years had passed since the Trojan War began and Neptune mourned his dead son, Hector, killed by Achilles. The sea-god asked Apollo to help get rid of Achilles, and so Apollo directed Paris' arrow to Achilles. When Achilles died, he didn't go to the Underworld. Instead, he went to Elysium because he was such a great hero.