Hyginus Fabulae, 107
After Hector's burial Achilles walked around the walls of Troy and proclaimed that he had sacked Troy singlehandedly. Apollo therefore was angered and disguised himself as Alexander Paris. He shot and killed Achilles with an arrow in the heel which is said to have been mortal. After Achilles was killed and handed over for burial, Telamonian Ajax demanded the Danaans give Achilles' weapons to him because they were cousins. Agamemnon and Menelaus took away the armor claiming Minerva's anger at him and gave it to Ulysses. Ajax was beset by madness and slaughtered his livestock then took his own life upon the sword which he had received from Hector as a gift when once they had fought hand-to-hand in battle.
— translation RTMacfarlane
107 Armorum Iudicium
Hectore sepulto cum Achilles circa moenia Troianorum uagaretur ac diceret se solum Troiam expugnasse, Apollo iratus Alexandrum Parin se simulans talum quem mortalem habuisse dicitur sagitta percussit et occidit.
Achille occiso ac sepulturae tradito Aiax Telamonius quod frater patruelis eius fuit postulauit a Danais ut arma sibi Achillis darent; quae ira Mineruae