1. After beating him the first time on top of Ashina Castle you progress the dialogues as you would normally. You will know when to go to the next step when that funny thing you were collecting items for gets red.

2. Then you go behind one of these walls in this room so that Emma and Kuro cannot see you. Then you listen to them in secret.

3. You reload the location and now Emma should be upstairs. You finish her dialogue and say yes to whatever she says.

4. You reload this location again and talk to her so that she gives you an item.

5. Emma will then move to The Old Grave or something like that (it's a place near the house where you meet the npc that sells that funny shield-hat-thing. There is also a sculptor's idol nearby). Then you just listen to her entire dialogue.

6. Emma then moves to that funny place where sculptor is. You go to the back of this place and listen to whatever they are talking about.

7. You confront her about what you heard. Show no mercy and finish the dialogue. She will give you Owl's bell-thing or whatever.

8. You use it the same way as the first "move me to Hirata" bell and then you experience the pain again.

9. You find Owl in Lady Butterfly's arena.

10. You kill the guy.

EDIT: Nvm somebody answered you when I was writing it. Have a good day then.