Immortality (or at least, invincibility) - he got this when his mother Thetis burned his mortal side (depending on you mythology, either she burned it with fire or rubbed it with ambrosia), unless someone hurt him in his fatal point (his foot).
Bravery - He is brave because he can lead in a war, just like Ares or Athena.


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 - I am not sure if I am correct or I am just speaking nonsense but based on what I can remember, I think that the mother of Achilles bath him in a river (I forgot the name) when he was still a child. The mother bath Achilles and the whole body EXCEPT Achilles's heel touch the water of the river. When Achilles grew up, he can not be defeated and the wounds struck on him heals. No one knew why it is like that.(obviously, we readers can assume that Achilles powers came from the water of the river that his mother used to bath him.) Achilles does not die when hit anywhere in his body except his heel.

Achilles is strong because like what I said, it is because of the water of the river.

Achilles can not be defeated because of the power of the water that touch him when he was a child.

This quality is just similar to "Unbeatable" but I included it because I am thinking that it means that Achilles can not be captured.
Achilles can not be captured because if someone dares to, he will fight him and most probably win. (except if his heel is hit)