New primary objective: Talk to Muiri
As Alain Dufont is dead, we can now take care of Nilsine Shatter-Shield and assassinate her. So exit the dwarven ruins of Raldbthar, open the world map and travel to Windhelm (screen above).
It is best to eliminate Nilsine during the night, because then streets of Windhelm are depopulated. Nilsine can be found in the western part of the town (screen above). If you want to avoid trouble with guards, you should kill her from hiding, stabbing her with the dagger or using a bow with an arrow poisoned thanks to Lotus Extract.
Another possibility is to kill Nilsine while she sleeps, but this involves one serious impediment. Go to the western part of the town and look for Shatter-Shield Manor (screen above). When you try to enter the building, it turns unfortunately out, that it has a very advanced lock, so your character must have highly developed thieving skills or be prepared to lose at least few lock-picks here.
If you've managed to open the clan's door, then crouch and head carefully north, finding the stairs leading to the upper floor. Locate the Nilsine's bedroom and slowly move close to her (screen above). Depending on your preferences you can kill Nilsine by stabbing her with the dagger or shooting her head with an arrow. After the successful action carefully exit the manor.
You can now leave Windhelm and return to Markarth. Same as previously you might take few moments to find Muiri. Initiate a conversation with her and tell her about eliminating both targets (screen above). The woman will reward you with gold and a very valuable Muiri's Ring.
New primary objective: Report back to Astrid
Leave Markarth and travel to the Dark Brotherhood's Sanctuary. Once you get inside the hideout, look for Astrid (she should stay in the first chamber) and talk to her (screen above). The assassin will have an unusual request for you. She will persuade you to hide inside the Night Mother's coffin to eavesdropping with whom and what Cicero speaks.
The Dark Brotherhood unlocked quest: Whispers in the Dark