Start by making your way to the Central Yharnam lamp and defeat the Beast Patient (Male) prowling around it for the Clawmark Rune. This Beast Patient (Male) is actually Gilbert, the NPC that handed over the Flamesprayer, and if you actually look at the window of the nearby house you'll see he busted out soon after transforming.
You can now make your way to the house where Viola's Daughter was located to speak with her Older Sister was located to speak with her Older Sister, if you choose the path that resulted in her death. If you choose to hand over the Red Messenger Ribbon you can reload the area and then take the ladder to find her dead and obtain the White Messenger Ribbon .
Make your way to the Grand Cathedral in Cathedral Ward to find Eileen the Crow near death and speak with her to gain the Wait gesture. You can then head inside the Grand Cathedral to encounter the NPC that beat her bloody and defeat him.
This NPC is particularly fast and difficult, with a single shot being capable of taking out the majority of your health. While he can be staggered with your firearm, actually hitting him can be difficult unless he is mid-attack, so you'll want to make sure that he is about to attack before you waste a bunch of bullets.
Sometimes he'll stop to buff himself up with swiftness spell, allowing him to teleport short distances to avoid attacks or perform some of his own, and other times he'll whip out a blade with a spurt of blood that does damage over time. Slow and steady wins this battle, as the NPC will also heal at least once, so you'll have to beat him down twice to actually defeat him.
Once defeated, you can return to Eileen for the Crow Hunter Badge and Hunter Oath to complete Eileen's quest line.
Returning to Iosefka's Clinic
Remember that ladder inside the cavern under Forbidden Woods? Well, if you return to this area and climb the ladders you'll find yourself behind the gate across from the Central Yharnam gate you opened at the beginning of the game.
Grab the Coldblood Dew (1) near the gate, which you can open with the nearby device, and then head through the opposite gate to continue. Head down the stairs into the plaza to kill a Brainsucker and then grab the Madman's Knowledge beside the well before climbing up the ladder. You can now cross the rooftops, dealing with the many Carrion Crows, to enter the back of Iosefka's Clinic.
As you explore Iosefka's Clinic you may run into a number of Celestial enemies, equal to the number of NPCs you have sent to Iosefka's Clinic, so carefully make your way right to enter the clinic room. Pick up the Cainhurst Summons before opening the clinic door that leads to the 1st Floor Sickroom lamp and then make your way to the opposite end of the clinic.
You can now make your way to the opposite end of the clinic, enter the room, grab the Communion Rune from the chest and then backtrack upstairs to find Iosefka, who is weakened by the Blood Moon and can be easily kill for the One Third of Umbilical Cord .