You have to keep Joseph injury free until he runs over to Kidman in the water trap and there is a brief cut scene following wires to the locking mechanism.
This is easier done on Casual difficulty or during a New Game +. Fortunately, Joseph tends to stand either in an alcove or with his back to a wall. All you have to do is kill the mobs before they get near him. I found it very effective to herd or line up several Haunted, hit them in the legs with a shotgun blast and burn the fallen group together. The hardest Haunted to stop are the dynamite tossing versions; however, if you hit them in the legs with your pistol they will fall over and drop the dynamite which will then explode.
Keep Joseph completely injury free (he can't take a single hit) until you unlock Kidman's trap and the Trophy will pop.