Recently I beat the Capra demon with a caster and here's how.
This seems a little too simple, but seriously, try it: as soon as the fight starts, do a roll directly to your right.
Examining the room, you can see that near the entrance (hidden by the camera when you enter ) is a weird little corner that makes it impossible to jump to the left and creates that annoying "Hey there! You're dead!" effect that Capra Demon tends to create.
The object in this fight is absolutely to make it to the stairs. When you are on the stairs,
- You can take out the dogs fairly easily
- Capra Demon pretty much can't hit you at all
- You can run up the stairs and then jump down them much faster than Capra Demon can chase you.
In other words, to win this fight:
Get to Stairs > Kill Dogs > Kill Capra Demon
Odds are Capra Demon is going to kill you before you get to the stairs, if you get there at all. Once you roll, keep your shield up and move quickly around him in a circle, and then back up the stairs.
Easier said than done, as you'll probably be taking some heavy damage! As I've said before, the real secret in this fight is to do a sudden jump to the right when you enter the room.
Don't wait for the Capra Demon or his dogs to attack or anything. Just move swiftly for the stairs.
You can get to the Capra Demon much faster by unlocking the door at the bottom of Lower Undead Burg and going to fight him via the female merchant who sells moss.