I once wrote that Achilles needs a meaning in life, and this is what I meant!!
He's not afraid of his own death. Not in the sense of a phobia, but rather a kind of anxiety, a reluctance to die. Death, early but dignified, is his own choice. It's a calming feeling on the outskirts of any battle, that death is somewhere near.
Achilles doesn't feel part of this world; the threads that bind him to the earth don't irritate his palms. Even Patroclus (inadvertently, but still) points this out, calling him a child of the sea and the rocks. Achilles isn't brave; he simply doesn't know the fear of death (his own, of course). And he doesn't give up his life only until someone needs it.
Patroclus is his root system, if you will, and Achilles is a beautiful, bright, eyesore of a barren flower with a single ovary inside. They are completely codependent, terrible and doomed, I hope they are happy in the afterlife, I hate them-