1. Get a spear or rapier type weapon. I preferred spear. Upgrade to 5. 2. Get a good shield. Heater shield or better. Upgrade to 5. 3. Use pine or fire resin. 4. Enter fog, dont move. Immediate target and toggle left to target on the dog running from stairs. 5. Capra and dog will jump towards you. Dodge left and poke dog. Dog dies. 6. Stay near the fog gate if you dont want to aggro the other dog. 7. You win.
It is the only fight next to the bed of chaos that's considered cheap. The very very first thing you gotta do is the down the dogs. Taking them down is fatal as if you kill them you basically won as the fight becomes incredibly easy. My advice: KILL THE DOGS
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Get a better shield and get down to light roll, upgrading a balder shield to +5 will allow you to guard the cappra's hits (most of them) and the rolls will help you dodge the dogs. This fight is decided in the first 5 seconds.
Kill the dogs first, then kite cappra around.
"Will the circle be unbroken, by and by, by and by? Is a better home awaiting, In the sky, in the sky?" ~ Elizabeth, Bioshock Infinite