This is the default ending that you can get by getting to Owl on top of Ashina Castle and choosing to 'Break the Iron Code, stay loyal to Kuro'. Defeat Owl, then speak to Kuro and you will be told to go to Fountainhead Palace.
Go to the cave at the back of the Corrupted Monk's boss arena in Ashina Depths and interact with the tent at the back to be taken to Fountainhead Palace. Make your way through the area and defeat the Divine Dragon at the end. Then head back to Kuro's Room and a second modified Ashina Castle, then backtrack to the initial Ashina Castle idol. From the idol, walk through the main gate and into the building on the left. Drop down the hole in the building and make your way to the Ashina Reservoir, fight a Seven Spears miniboss, then enter the secret passage to fight the final boss.
Defeat him, then give Kuro only the Dragon's Tears to get this ending.
There is also a method to get this and the other two ending achievements without having to play through the game three times. Once you defeat Sword Saint, save and quit back to the dash and then reenter the game again. Choose to give Kuro the items for the ending you need, then once the achievement pops (when the credits start), hit Guide, press
on Sekiro, choose Manage Game & Add-Ons, scroll down to Saved Data, and choose your saved data, then Delete from Console. Repeat until your data is gone. Now restart the game and you will be able to choose again. Repeat for the other ending to get all three.