How do you Capra demon? I swear I've been trying to kill him for over a year.
If you can one-hit-kill the dogs, enough poise to take a bite from the dogs without staggering will work. The number one enemy in this fight is being staggered by the dogs long enough for Capra to hit you.
As soon as you enter the fog, take a couple steps forward and roll through Capra's first attack, then immediately swing for the first dog. He'll probably be biting you at this point, but this is where the poise comes in. As long as you can get the hit in without being staggered, the minimal damage from the bite is irrelevant.
Once doggy #1 is dead, roll past Capra and kill doggy #2 as quickly as possible. If you were reasonably quick with the first part, the dog should still be in the back right corner with his thumb up his ass. Again, poise keeps you from being staggered by their bites while you kill them. With both dogs down, it's one-on-one, which is easy mode.
This is how I do the fight every time, and it has never failed me.