You'll need a vial of Zyme for this one and a save in the NYC area during JC's second visit, where he needs to find Paul.
Follow the instructions for this achievement up until "the conversation will take a turn for the worse":
Just before Jojo opens fire at Gilbert, use the vial of Zyme and let Jojo kill Gilbert. This will unlock "What a Shame", but since you were on Zyme, this achievement will unlock as well.
Managing to kill Jojo while JC is still under the influence will unlock: