YOu take the Quest to killl the Orphanage Owner( the Kind)
When the Dark Brother abducts you after that you kill Astrid instead of one of the People with hoods on and then report that you killed Astrid to Commander Maro in Dragon Birdge
Destroy the DB =/= "Good". It's effectively impossible to be anything truely "good" in Skyrim.
In addition, it's also impossible to fully destroy the DB, seeing how Babette, Cicero and the Night Mother all survive.
also this.