This is a very interesting approach by Zynga on the new Boss Fights they have been advertising and pushing. Each fight requires nothing but consumables. You can't use Stamina to fight the boss and your account strength seemingly has nothing to do with how much damage you cause. I recommend asking for Shotgun Blasts as often as possible from your mafia as they do the most damage. You can even click on your own post for help and receive 2 of them. Many mafia members have reported beating all three tiers using Shotgun Blasts alone.
Each consumable does a different amount of damage and there are 3 combos you need to use while fighting the Boss to get the Rafael achievement. See the previous post on Roughhouse Rafael Mission Walkthrough for info about unlocking the 3rd combo. Here are the 3 combos you need to perform:
If you do the 3rd one before finishing the 2nd step of the related mission, YOU WILL NOT GET CREDIT! If you perform all three combos before defeating the boss and have the 3rd unlocked from the mission, you will get the new Achievement:
The Health levels for the bosses are 15,000 for Bronze, 25,000 for Silver and 35,000 for Gold Mastery. Pretty good loot for finishing.
Have fun and Happy Hunting!!!