To access this room you have to kill the two dancing splicers in his apartment located here:
Cohen will get angry and come down to attack you, and the door will now be unlocked. You need to enter the room and head up the stairs for the achievement to pop. As far as I know, this is not available if you chose to kill Cohen after completing his "masterpiece" to open the second treasure. If it is available, please let me know in a comment.
The room contains a Power to the People machine, so you need to get access to this room to be able to fully upgrade all weapons as well.