You have to take out the 2 electrical things on his back. When you hit them you will get a critical hit. It won't look like you are doing a lot of damage until you take one out then a massive amount of health will go away. Then after both are gone he will shoot this blue electrical stuff out of his chest. When he does you have to shoot him there it will also register as a critical hit when you hit him there. If you are hitting him anywhere else he will just deflect the bullets and it will cause no damage.

1. First blue electrical pack on back
2. Second blue electrical pack on back
3. Chest when he is standing up shooting electricity

It took me a few times of dying and aggravation to finish it.

If you have the bee shield and a weapon like the Maggie I strongly suggest using them. It helps tremendously.