You need a +10 fire weapon. This path adds fire damage to your weapon.
Large Fire Ember: Found in the area between the Ceaseless Discharge boss and the Demon Firesage, to the left of the fog gate and it is guarded by two Taurus Demon mini bosses and four ambushing Burrowing Rockworms.
After you have obtained this ember, you need to bring it to Vamos the blacksmith in the Catacombs. In the end, you need the materials listed below.
Titanite Shards x9 - Purchased from Andre of Astora in the Undead Parish.
Green Titanite Shards x10 - Purchased from the giant blacksmith in Anor Londo.
Red Titanite Chunks x7 - Farmed from Chaos Eaters in Lost Izalith or a guaranteed drop from the greatsword wielding Black Knight in the Kiln of the First Flame.
Red Titanite Slab - Obtained from a chest in Lost Izalith (VIDEO) or trade an upgraded Ascended Pyromancy Flame with Snuggly the Crow.