When fighting George, you'll see barrels of light, lure him close to one and shoot it, this will cause George to fall. Use this time to shoot him as much as possible with your strongest gun (I opted to placing 3 red gems into my Boner's damage and that's it). Depending on the difficulty, gun strength and capacity, it may take up to 6 or 7 barrels + full clips to take him out (but this was on Legion (Hard) difficulty).
When he steals the goat, which is hilarious to me for some unknown reason, simply look into the sky to see the beam of light, this is where George has taken that poor goat. Follow it and use your LightShot on it to chase away the darkness.