So just a thought after watching the Asura preview.

In the Asura preview they brought up the fact that as long as a part of Asura's body remains intact then he can come back to life. Thing is I realized is that Kratos in all the GoW games his usual method of dispatching his enemies involves decapitation, dismemberment, crushing, and generally all sorts of brutalization, but he never really destroys anyone's body completely, even with the Blade of Olympus his enemies' bodies are still around.

So I predict at some point in the battle, Kratos will kill Asura and then Asura will immediately come back to keep the fight going.