The only large guy that I find troublesome would be Handymen. Patriots can be mind controlled as well as turrets, and the latter takes very few shots to destroy. Patriots are a bit more resilient, but you can damage them while they're mind controlled.
I'm trying to figure out some good ways to use my vigors to help me out. Most boss battles aren't that hard, but Handymen are just a huge pain in the rear. The biggest problem is that I keep forgetting that the game is
usually nice enough to give me a RPG
somewhere in the large area where I'm fighting. The problem is that I never think to look for it!
One thing I want to do is upgrade the Charge vigor. The one upgrade makes you invulnerable and restores your shield upon charging, and the other adds an explosion after you charge. Handymen are weak to explosions, so I can zap him with my upgraded Shock Jockey (increased stun time), and then charge him. I also use the hat that gives you 4 seconds of invulnerability when you use any health restoration item. That invulnerability has no cooldown and even works on simple food items. So, if my health is low, sometimes, I will just scour bodies for food.
Sad. :'( I'm at the (not much of a spoiler, but I'll tag it anyway)
right now, so I think I'm doing a bit better. I also think I finally have all the vigors, and I'm trying to find the best way to use them at this point.