This is story related and cannot be missed. The achievement does not unlock, though, at the point where the Butcher is turned over to Burke. Rather, it pops after a cut scene with Jonathan Maguire, the former Assistant Director of the Criminal Enterprise Branch. Following the cut scene, a banner appears stating that the
Kill the Bishop mission is complete and the achievement pops as shown in the below video:
The story progression that unlocks the achievement is completing the Pointe Verdun missions. The specific trigger is the
Kill the Butcher mission. The prerequisites for that mission are to complete the
Cut and Run and
A Nation Once Again missions and to secure the Moonshine and Protection rackets. All of these take place in Pointe Verdun. Once the
Kill the Butcher mission is completed and the ensuing cut scenes play out, the achievement will unlock: