For me there are a couple of possibilities. Either Bran takes the Night King out with some mind tricks ... remember the Night King touched Bran when he was in that mode, so the other way round should be possible too, or Arya takes out the Night King with little fingers dagger.
I think with the Night King gone, all his minions will shatter and turn to dust in 1 instant ..... job done. So there doesn't need to be an almighty battle, it can just be 1 single blow. The other alternative is that Danny takes him out with her dragons ... it has to be something like that