This achievement has two parts, the first one being in Brooklyn Bridge Station and the other in Paris, two chapters which are quite far from one another, so make sure you don't get confused with your saves.
1) Brooklyn Bridge Station: The upper floor from where you enter the station is occupied by the Rooks, a gang whose members all wear the same blue clothes. You need to kill all of these gang members, they're all on that floor, with the exception of their leader, El Rey. I don't know if that voids the achievement, but try not to kill any of the female gang members. Once they are all dead, go towards the one side of that floor, where you should find El Rey. If you came up to just some cardboard boxes, you're simply at the other end of the floor. Talk to him and select the dialogue option "Just hand over the LAM, punk". El Rey will give JC the LAM as a sign of peace, triggering the dialogue we want. Watch out as El Rey becomes hostile once you've moved away from him. Regardless, we've gotten what we want from him, so you're free to kill him, knock him out or simply run away if possible.
2) La Porte de l'Enfer nightclub: After getting in the club whichever way you are able to in an attempt to find Nicolette DuClare, there's a woman hanging around on her own on the upper floor, that's Cassandra. We're not interested in the dancing nurse nearby. If you talk to Cassandra, she offers you the code to the club's storage room, for a price of course. Either refuse to pay her or don't speak to her at all. Go towards the bar on the ground floor level and you will easily notice a doorway behind the barman, next to it should be a mech bodyguard. Simply walk in there, nobody turns hostile. Go to the right and you'll come up to a door with a keycode. The code is 1966. You need to enter that room and you'll know the game registered you did so if the exploration bonus appears in the upper left corner of the screen. Loot whichever items you want, then find Cassandra. The dialogue has only one possible outcome and the achievement unlocks before it finishes.