The third part of Slash's quest involves finding him (again) in a green exclamation point room on the map in the Factory (seems familiar). When you find him again, this time he will be trapped in a laser barrier and will ask you to kill him or leave him alone. In order to progress his quest line and get this achievement; you have to attack the orange computer in the same room with an electric weapon. This means that you have to be lucky enough on your run to find him and an electric weapon. To make it slightly easier on yourself; you can begin a new run and hope to get an electric weapon in the first room, if you don't then restart the run by quitting to the main menu and try for an electric weapon again until you get one. If you kill him here - or at any point in his quest line - then he will be reset and return to Factory, waiting to fight you.