Who was Achilles wife?

It may be Briseis, though, in the books, she was never referred to as Achilles' wife.

Briseis's real name was Hippodameia, "Briseis" being a patronym as a daughter of Briseus.

Brisēís (Greek Βρισηίς) was a Trojan widow (from Lyrnessus) who was abducted during the Trojan War by Achilles upon the death of her three brothers and husband, King Mynes of Lyrnessus, in the fight.

In Homer, Briseis is Achilles' captive, given to him by the Greek army as a prize. He also loves her, comparing their relationship with that of man and wife, and is angry at the thought that Agamemnon sleeps with her. When the quarrel is resolved, Agamemnon swears to Achilles that he has never slept with Briseis.

Some also said he married Medea, and that after both their deaths they were united in the Elysian Fields of Hades - as Hera promised Thetis in Apollonius' Argonautica, though, in other books, Medea is wife to Jason (of the Argonauts).

Others say that Achilles' wife is Deidamea. Achilles' mother foretold many years before Achilles birth that there would be a great war. She saw that her only son was to die if he fought in the war. She sought a place for him to avoid fighting in the Trojan War, due to a prophecy of his death in the conflict. She disguised him as a woman in the court of Lycomedes, the King of Scyros. During that time, he had an affair with the princess, Deidamea, who then gave birth to Neoptolemus. Neoptolemus was originally called Pyrrhus, because the female version of that name, Pyrrha, had been taken by his father while disguised as a woman.