Uhmm. I used the Light Machine Gun with Special 38. Dropped him on one salvo
Guns 100, Anti-Materiel Rifle. nuff' said
It doesn't matter really. Just get a long range weapon, sneak, then clock his dome. Thats what I did
Any weapons with Silencer attached to them would be much easier. or 'Very' powerful weapon, such as Missile Launcher, Tesla Cannon or Anti-Materiel Rifle would be another good choice. And, if you use a Stealthboy, Things would go easier and easier.
Or what I did was make it to Freeside and get the King's dog Rex and had Rex attack him. This strategy can work with any companion actually really. But be careful if you are on hardcore mode and your companion dies you lose him forever.