On the battlefield, he is unstoppable, able to rout whole armies single-handedly.
He suffered from an overweening pride, called Hubris, which seemed to be a common characteristic of many Greek heroes. Achilles is also an exceedingly proud person. When the Greek general Agamemon takes Achilles' war prizes for his own, Achilles' hurt pride causes him to declare that he will no longer fight for the Greek side.
He is seen as impetuous, but loving to his closest comrades (Patroclos, Phoinix, Antilochus) and an honorable man (through the compassionate mercy he showed to Priam in returning Hector's body).
Achilles was also very selfish.
He asks his mother, the goddess Thetis, to ask Zeus to strengthen the Trojans while weakening the Greeks. He wants Agamemnon and the Greeks to realize how much they need him.
The turning point is when Patroclus, Achilles' beloved cousin and friend, borrows Achilles' armor and is killed in battle because of it. At this point, Achilles' rage becomes the rage of revenge and love. His capacity for such personal loyalty complicates the vision of a simple hero looking for kleos.
Achilles is a person who is capable of great anger
He is arrogant in that he thinks that he is bigger than the entire war that the Greeks are having. If Agammenon is going to take Briseis, Achilles is going to be too arrogant to help the Greeks.
Finally, he is loyal -- at least to his friends. He fights and kills and eventually dies to take revenge for Patroclus's death.
Ultimately, he is willing to sacrifice everything else so that his name will be remembered.
Achilles - The son of the military man Peleus and the sea-nymph Thetis. The most powerful warrior in The Iliad, Achilles commands the Myrmidons, soldiers from his homeland of Phthia in Greece.
At his birth, his mother had dipped him in the Styx, so that all parts of his body are invulnerable to hurt except the heel by which she held him. A young man