Destroy all the screens in the room to defeat Wrightson. You can only destroy them when they are firing. Just dodge the ray and shoot them. Be sure to also, avoid the Aura Beasts in the room.
When the fight starts, run forwards and to the right hand side of Nicholas Wrightson, so that you are positioned against the wall and can see the screens the he uses to fire laser beams at you. When there, use your machine gun or assault rifle on the screens. They will explode, and you will take little damage. The screens cannot hit you without hitting another screen. Watch out for Aura Beasts, but they are not too difficult. It is possible to defeat this Boss in under thirty seconds, even under the elite difficulty setting.