During your third and final visit to Hell's Kitchen, follow the main quest and speak with Harley Filbin in the underworld bar. He'll warn you that Joe Greene is an informant for UNATCO and ask you to take care of him. Head to the free clinic and find Greene in a corner in the main area. Talk with him making sure you choose the dialogue option that exposes him rather than accuses him. Then either kill or incapacitate him to receive the achievement.