You encounter William twice in the game, and face 3 of his stages. 
You face him in his second when you are going to the lab, you need 
heavy guns, Claire should use the grenade launcher (loaded with 
acid and flame rounds of course), because the spark shot has too 
much recoil and a limited range, so you'll end up using more health 
items than needed, and Leon should use his Custom shotgun and a 
little magnum wouldn't hurt, though you really don't want to use 
more than a clip. put distance between you and William so you can 
plug him from a safe distance, and stay to a side of the walkway, 
so if he gets close, you have a change to juke him and run along 
the other side, repeat as necessary. (Leon can even use his Custom 
handgun, if you found the parts, on automatic)