Steps 1 and 2 can be completed after defeating The Owl, but if not done up to this point, it is highly recommended to do them immediately after defeating him. Simply eavesdrop on Kuro as many times as you can, rest, talk to Emma/Kuro, resting each time, until Emma moves upstairs. The key here is talking to Kuro until the topic becomes the Mortal Blade.
After defeating Genichiro at the top of Ashina Castle and getting Mortal Blade from The Divine Child, exhaust all dialogues with Kuro and Emma, and exhaust all eavesdrop opportunities on Kuro, which you get when hiding behind a wall using Hug Wall mechanic. The specific location for eavesdropping requires the player to stand just around the corner behind Kuro and the large statue he stands next to. Go around behind the statue and then hug the wall on the left side of it. Multiple rests and switching from one to another may be required. Technically the player must only talk to Kuro about the Mortal Blade then hear a specific eavesdrop conversation which alludes to him keeping a secret from Sekiro, but this may not trigger immediately as many dialogues become available at this point - simply exhaust all available conversations/eavesdrops.
Progress the story and collect the Lotus of the Palace and the Shelter Stone key items. At this point you will face new Interior Ministry Ninjas at Ashina Castle.
At the top of Ashina Castle, The Owl will give you the choice to follow the Iron Code or to continue to serve Kuro, the Divine Heir. Choose to continue to serve Kuro and defeat The Owl.
Exhaust all available conversations/eavesdrops again, and rest to nearby statue causing Emma moves from her current location to the top of the stairs.
Talk with Emma at the top of the stairs, pick the option to keep Kuro alive, then rest at nearby statue, talk to Emma again at the top of the stairs and agree to help her, she will gives you Tomoe's Note.
Travel to the Old Grave Idol and go to the left, you will find Emma standing infront of two tombstones. Talk to Emma and then travel to Dilapidated Temple.
Eavesdrop on Emma and Sculptor from behind the temple. Talk to Emma and then choose "Ask about what you overheard", and then, "What are you hiding?" to receive Father's Bell Charm. Use it at the Buddha statue. If you haven't completed Hirata Estate area, you will need to do it by killing Lady Butterfly before you can use Father's Charm.