Shivs were doing 270 damage and Grenades about 190. So, just from using my 10 Grenades and 10 Shivs, I had Halloran down 25% from his starting health. This was going to be too easy!
But this was far from a blowout fight. My Stun Guns were not as helpful as before. They only gave me one free shot at Halloran, instead of two, and each attack of mine only did slighly more than 400 damage.
By contrast, my henchmen again went down whenever Halloran sneezed, and my 600 Health points were wiped away any time Halloran hit me directly. So Health Kits were essentially useless here.
Still, after using the 10 Stun Guns, and recharging a *number* of times, the end was near:

And at last, Governor Halloran has been recalled from office.

You get a nice 2,200 XP bump and the Ruby level Hallorans Helicopter has impressive (120/190) stats.

Some commentors have correctly noted that there is no reason to use your Stun Guns, Shivs, or Grenades since you can simply go to Moscow or Cuba and recharge your health with the otherwise-useless currency there. That begs the question of what exactly one WOULD use the Stun Guns and other Boss consumables for...
Either way, once you're done with Governor Halloran at Ruby level, and assuming you've gone through the Las Vegas Distrcits in order, you're all out of Bosses. For now...
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Here's the Governor as he appears in the Boss fight. He has 14,000 energy and no henchmen. Sounds easy, right? Well, the Shivs do little damage (maybe 30 points) - same with Grenads. This is one of those fights where you need to use pretty much all Stun Guns, and not let him attack at all - use the Stun Gun, attack, repeat. DON'T ATTACK TWICE AND LET HIM HIT YOU. ------Why? As I found out the hard way, the Governor's first attack did NO damage to my two henchmen (who usually get wiped out in one shot anyway) and went directly to me, taking most of my 520 health with it. I furiously clicked on my Health Kits and then went into Stun Gun overdrive. You can also call for help on this job, and of course, come back and finish him off, to be treated to:
1,800 experience points is a sweet boost, and the Silver Level Hallorans Helicopter stats are an impressive 100/160 - your top defensive vehicle. For now, I'm staying put on Silver, loading up on the great offensive loot there, and pledging not to move to Gold Level District 8 until the Challenge Mission: Dublin and the Prized Pigs challenge are complete.

