As seen in The Penthesileiad
Best of the AchaeansAchilles is a Prince of Phthia, the son of an adventurer and a goddess, recruited by Agamemnon to be the powerhouse of the Achaean mission to wreak vengeance on Troy. Through his mother, Achilles has some knowledge of his own destiny, including a few details about the timing and circumstances of his own death before the end of the Trojan War.
FamilyAchilles is the product of an arranged marriage between the mortal King Peleus of Phthia and the sea goddess Thetis. His parents became effectively separated on the night their marriage was consumated, and a newborn Achilles was dumped on Peleus's doorstep nine months later with a note reading, "I believe this thing belongs to you. I made it (mostly) invulnerable. You're welcome." Achilles still has the note in his possession. Achilles was raised side-by-side with his foster brother, Patroclus. Both boys were tutored by Phoenix, at first, before Achilles showed special aptitude for fighting and was sent for "finishing" to his father's alma mater, the cave of Chiron the Centaur. When word of the boy's progress reached agents of Agamemnon, Achilles was put at the top of the recruiting list for the Achaean campaign against Troy. In an attempt to protect her son from a fate worse than or equal to death, Thetis snatched the boy from Chiron's grove and brought him to the island of Skyros, where he might pass for a tall, muscular, hairy-legged maiden for the duration of the war. Achilles was outed as a man due to the cleverness of Odysseus, but not before he'd secretly married Princess Deidamia, the daughter of King Lycomedes, and fathered a son, Neoptolemus.
AppearanceAccording to classical sources, Achilles is the biggest, most powerful, most physically imposing man to ever put on a dress and pass for a teen girl. His most noteworthy feature is his "flame-colored" hair, which may have either been red, yellow, or white, depending on how hot of a flame the ancient poets were describing.
PersonalityIn the Penthesileiad, Achilles is still coming to grips with events of the Iliad, including the death of his closest friend, Patroclus, for whom he feels personally responsible, not to mention his own rapidly approaching demise. (Seriously, don't mention it, mortality is kind of a sore spot for him.) Achilles tends to deal with his problems by withdrawing from Achaean society in a melancholy yet musical way. If Achilles tends to think highly of himself, it's not without cause. He will speak truth to power when he feels a commanding officer is in the wrong, but he's also been known to have a bit of a temper and to hold a grudge.
Fighting StyleAchilles is the strongest warrior on either side of the battlefield. He has the best armor and shield, crafted for him by Hephaestus himself. He is practically invulnerable (except for the back of one heel). He carries a spear that that no other man is fit to lift, given to Peleus by the centaur Chiron. He fights like he's running out of time and knows that he will not survive to see the ultimate fall of his enemies.
Military RoleAchilles reports directly to Agamemnon. He commands 50 ships of about 2,500 elite Myrmidon warriors loyal to his father, Peleus. In battle, Achilles likes to fight in champion mode, armed and equipped by his valet, Alcimus, and driven by his charioteer, Automedon. Achilles has delegated command of his Myrmidon troops equally among five battlefield lieutenants: Menesthius, Eudorus, Peisander, Phoenix and Alcimedon. Unlike most of the Achaean commanders, Achilles was not one of Helen's suitors, and so is not bound by the Oath of Tyndareus. He and all of the troops pledged to him are free to leave at any time.
In the Mythoversal PenthesileiadThe Quintan Penthesileiad keeps Achilles on the sidelines for most of the story, while the Mythoversal Penthesileiad shows a healthy interest in what he's been up to and why he's been kept from the fight. We first meet Achilles in "The Life That's Been Erased" in The Penthesileiad where he laments the loss of his closest friend. Thereafter, he rebuffs an embassy of Achaeans over the course of three non-consecutive chapters:
In the Epic CycleThe Iliad largely centers around Achilles, to the point where the entire work could reasonably be subtitled, "That time Achilles lost his cool for a while." Achilles then appears in the first two-and-a-half books of the Quintan Posthomerica, a 4th-ish Century retelling of stories from the long-lost 8th Century BCE Aethiopis of Arctinus Milesius.
Death by arrow, perhaps in the heel (or not), shot by Paris (or maybe by Apollo himself). Although dead, Achilles's legacy is felt throughout the remainder of the Posthomerica, and his spirit must be mollifed with a human sacrifice in the last chapter before the Achaeans are allowed to leave the Troad plain. In Homer's Odyssey, the ghost of Achilles makes a final appearance when Odysseus visits the Underworld. Famously, Achilles wishes that he could be alive again.