This is the true ending to Bloodborne. You first need to get all 3 pieces of the "One Third of Umbilical Cord". Once you have them, you want to consume them all by selecting "Use" on them in your inventory. Doing so will give you some insight, but they are needed for the secret ending. Spoilers are ahead. Proceed at your own risk.
*** Spoiler - click to reveal ***
You then want to go to the Hunters Dream and then through the gates. Make sure you have all One Third of Umbilical Cords & used them. Going passed the gate marks a point of no return. Then go refuse Gehrman and fight him. Once you beat him, you will need to fight Moon Presence. This is a fairly easy boss and shouldn't take too long to kill. if it does kill you, you will respawn back in the hunters dream and will be able to fight him straight away. You don't need to fight Gehrman again. Upon the death of the Moon Presence, a cutscene will play out and the trophy will unlock.
Here's a video guide of how to get the all of the One Third of Umbilical Cords.
The first one you can’t miss, it drops off the Wet Nurse boss.
For the second, you'll need access to the Abandoned Old Workshop. Which can be accessed from the Cathedral Ward area.
*** Spoiler - click to reveal ***You must defeat the "Blood-Starved Beast" first! He can be found in the Old Yharnam area. After this boss is dead a new door will open up at the spawn point of the Cathedral Ward. Go through the door on the right and use the elevator to get upstairs. You must then drop down a ledge on the right side of the tower. Now go inside the tower (where it's really dark and there are lots of wooden platforms). There is a tiny platform on the wall of the tower. You must roll down onto this platform. Be sure you have enough health or you will die from the fall!
After you've made it to the wooden platform you just need to drop down to the gate, open it, and enter the abandoned workshop area.
For the third, you'll need access to the top of Iosefka's Clinic. Here's a video to get you there. This one is missable.
*** Spoiler - click to reveal ***Do not go for this piece of the cord before killing Rom, the Vacuous Spider or before killing the Shadow of Yharnam. You can go to Iosefka's Clinic before Rom, just make sure you don't actually kill the woman until after Rom is dead.
There is a fourth One Third of Umbilical Cord. But you only need three for the trophy.
*** Spoiler - click to reveal ***If you did happen to go to Iosefka's Clinic before killing Rom, and before killing the Shadow of Yharnam (If you have already killed this boss then it is too late for Arianna, as she will have been killed by the man across the street). Because of this, this cord is missable.
What you want to do is first, is speak to the old woman lying on the floor in the Cathedral Ward. She'll say if you find anybody, you can send them here as it's a safe place. Next, you want to go and speak to Arianna as soon as you open up the gate using the Hunter's Emblem in the Cathedral Ward. You want to go left here past the enemy with the flamethrower and down the stairs into the foggy street below. At the very end of this alleyway, you will find Arianna by interacting with the last door on the left. She will ask if there are any safe places, tell here to go to the Cathedral Ward. If you tell her to go to the Clinic, she will die before you can get the cord from her.
Arianna will now sit in the Cathedral Ward, and she won't really do much from here on out. But, there are a few things you need to be careful of. There is a man in the Forbidden Woods who you can send to a safe place, but he is a werewolf so you do not want to send him to the church. If you do he will kill Arianna. There is also a woman at the bottom of Hypogeon Gaol that you can save if you are wearing any church clothing items. She will also kill Arianna. To be safe, don't send anybody back to the Cathedral Ward if you come across them. You won't get anything for sending people there anyway, so it's better to be safe then sorry.
After you kill the One Reborn and enter Mergo's Loft, you can now get the cord from Arianna. Go back to the Cathedral Ward and he will have moved from the chair she was in before. You want to go down the ladder behind you and she will be sitting in a corner, and there is a baby great one on the floor. Simply kill the great one and it will drop a piece of the umbilical cord.