I don't recall how I beat it the first time 'round. I think I had a +3 Claymore and just swung it until the darn thing keeled over.
The Capra Demon, for its timing, is one of the most difficult bosses in the game due to the small dog adds. The dogs can interrupt your attacks, or just lock you down long enough for the Capra Demon to get one of its swings in and drop you. Thankfully, the environment is well positioned for cheese strategies.
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