Oscar entered the boss room through the giant door near the bonfire with his sword and shield equipped. He was not wearing his usual armor in order to increase his movement speed.
After seeing Oscar enter the Asylum Demon jumped down from the roof. The impact from the Asylum Demon landing shock the ground itself. The demon then performed a vertical attack with his great hammer but Oscar dodged it by jumping away from the demon.
While that was going on the female undead moved to the ledge and started firing arrows at the demon. The demon was now under attack from 2 directions. When the demon focused on the archer then Oscar would get the chance to attack and Oscar's attacks were much more damaging then the arrows so the demon focus was on him now.
For the next few minutes Oscar kept running away from the demon's attacks and the female undead would keep firing here arrows at the demon from above. The demon never had a chance of winning and as expected it died. After the demon's body disappeared it left behind his Demon's Great Hammer, Big Pilgrim's Key, and a Humanity.
John unlocked the giant door leading to the ledge with the key and then gave it to the female undead along with the hammer and the humanity. Because of her inventory she was now John's baggage carrier.
They then walked to the edge of the cliff and a giant bird which arrived out of nowhere grabbed them in its claws and carried them to Firelink Shrine. John was worried about getting injured by the bird but their was nothing to worry about since the bird's grip was very loose.