Stage I
The first stage of this battle becomes significantly easier once you understand its mechanics. There are a multitude of Deacons of the Deep in the area, and the “boss” doesn’t take any damage when you hurt or even kill them. Instead, you have to kill the Deacon of the Deep that is glowing red to deal any permanent damage to your enemy. You can kill the other targets temporarily, but they’ll return shortly.
Thus, rush for the glowing Deacon of the Deep, hack it apart, and then back off so that you can spot the red light descending on the next active Deacon of the Deep. Enemy damage output is minor, so you are going to be fine as long as you have a couple of flasks to spare throughout the fight.
Stage II
After you get the boss to half health, the light recedes once again. It returns as a new challenger is summoned. This is the Archdeacon, and he’ll be surrounded by a few tougher Deacons of the Deep in blue. As before, you can only deal lasting damage by hurting the glowing target. This time, you won’t have to shift your focus. Archdeacon Royce is the real enemy, and his death ends the battle.
Use extremely long combos to deal maximum damage. These adversaries can’t interrupt you very well, nor can they outdo your damage output. Make this a battle of extended trades. Combo hard, back off, heal, and repeat. This isn’t a time for finesse.
Use the Bonfire that appears after the fight, and loot the Archdeacon Armor Set from a body on the floor. You’re now finished in the cathedral. Proceed to the Catacombs of Carthus. If you’ve beaten that area already, make your way over to Irithyll instead.