The Capra Demon is the boss of the Lower Undead Burg. You can get to him either by going left, down to the end of the main street (past the Undead Assassins and Undead Dogs), or by going through the shortcut in the waterway in the Firelink Shrine after you unlock it.
This boss is highly susceptible to fire, therefore, any variation of the Firebomb or a Charcoal Pine Resin-coated weapon, will go a long way.
This particular boss is later found in packs, in the Demon Ruins, where they can be farmed for a decent amount of souls, and potentially, their weapon.
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