Curly Bill is one tough boss and he might prove to be somehow unbeatable at first. But just because he's tough, doesn't mean he's smart. And we are going to kill him the smart way.
First, with which weapons I defeated Curly Bill: - Akimbo sixshooters - Dynamite - Rifle Tho' I bet a shotgun would prove to be more useful at this stage, I guess you can test it out.
The first thing about Curly Bill is that he's fast. Even if you are in cover, he will start to run around the entire map, and because of the enviroment you are in, you will often lose him from the line of your sight.
Second thing is that he literally eats bullets, especially revolver bullets (dynamite - not so much).
The third thing is that he manages to kill you in almost an instant and you don't have any time to react, especially if you are close to him. Besides, from time to time, his minion Cowboy comes around and starts shooting you.
Now that we have the background and all the necessary info, let's talk about tactics.
As I have pointed out before the three main strenghts of Billy's, now we need to counter them somehow.
Billy's mobility is propably the weirdest thing about him. He manages to run so fast, that sometimes I ended up thinking that he's able to teleport across the location. It's mainly due to the small area in which you fight and it allows him to run around you.
You should be mostly running away from him, rather than try to face him in close combat. I know that it might sound utterly stupid, but I think it might be the only way. Billy will try to shorten the distance between you and him, thus' you need to keep on running away to cover. And since there's a lot of stuff to hide behind, it shouldn't be a problem. You shouldn't also run when he's shooting at you, even if you are in cover. If he's not, then change your position. I repeated this mistake of running while he was shooting at me, over and over again, and it was the main cause of my deaths.
The first time you look at Billy's life bar, you think "Hah, he'll be easy!" but the moment you start shooting, you realize he doesn't care that you are shooting at him. Thus' a tactic known from many games applies that you need to "hit and run" because his shots are deadly (sometimes he can kill you in a short burst, if you are close enough). Basically, when Billy's running or reloading, you fire everything you have at him and then run away, so he won't be able to get you. But you have an ace up your sleeve, and that is the bullet time, which you activate by pressing Q. Make sure you have your guns reloaded and that Billy is not shooting at you and that he won't run away. Then, press Q and fire everything you have at him (most likely pistols/rifle/shotgun, haven't tried out dynamite). You can also throw dynamite at him if he's reloading, but I'd rather save it for the annoying minion. Billy calls out for his cowboy friends to help him out and you have to deal with them too. They are the "average" enemies, so just either throw dynamite at them or shoot them (headshots should kill them in an instant).
And that's all folks! Billy is not the hardest boss in video game history, but he can prove quite annoying if proper tactics aren't applied. This is of course my way of beating him, you can test out your own and post it in the comments or even create a seperate guide! Call of Juarez: Gunslinger is an amazing game and I hope Techland will provide us with such quality every year. :)