Achilles' main flaws are his anger and his pride. He is easily angered, and when he is angry, he is often violent. He is also very proud, and he often refuses to listen to advice from others. These flaws lead Achilles to make several mistakes that have consequences for himself and others.
For example, Achilles' anger leads him to quarrel with Agamemnon, the leader of the Greek army. This quarrel leads to Achilles withdrawing from the battle, which has disastrous consequences for the Greeks. Achilles' pride also leads him to refuse to fight against Hector, the greatest warrior of the Trojans. This decision allows Hector to kill Patroclus, Achilles' closest friend. Achilles' grief over Patroclus' death leads him to return to battle and kill Hector, but it also makes him even more violent and bloodthirsty.
Despite his flaws, Achilles is still a heroic figure. He is brave, strong, and honorable. He is also loyal to his friends and family. His flaws make him more relatable and human, and they add depth and complexity to his character.