I think that quest is a bit misleading, the map changed a while ago and the nightclub used to be in Downtown, sadly there's not a lot of content for Alice right now, but yeah, her scene at the nightclub, at Adrian's room, at the beach if you went for the steal route and at the church if you share is all there is for now.
To become a living weapon you need to go to the shrine once a day and kill all three demons, do that until the blue-haired demon comes to you, resist her and talk with the Master, you'll get the living weapon trait after that.