Weird West: Definitive Edition

Missable if you bypass the side quest or get spotted.
Near the start of Chapter 2 (when you're a Pigman) you'll be asked to visit "Quigley's Lantern Rooms" just north east of Grackle. Once here ring the door bell, give the old lady the VIP password and then speak to the lady in the window above. She'll ask to meet you round the back. Once you move round the back let the dialogue play out and agree to help kill Maximo.

I suggest climbing onto the roof for the quickest and easiest method. Do do this pickup the Barrel round the corner and put it against the Pigsty fence. Climb onto the fence, then the balcony above and then the roof. You may need at least 1 point in the jump perk to reach it. Once on the roof move towards Maximo (blue triangle) and drop onto the balcony beside him. Enter the door, this room is safe as no one ever enters. Quick save here.

Now let the dialogue play out with the worker so she leaves the room. Time the guard patrol and enter his room. Knock him out and retrace your steps back into the "safe" room. Throw him off the balcony undetected and job done! Jump down and leave the area - the achievement should now pop.

See my video for the full guide:

To get this achievement you have to knock out and throw the bordel owner of The Lantern Room from a balcony. You need to do this without beeing observed, so this is a stealth mission. The mission is in the second act of the game where

This is how i solved this:
Go up to the front door and ring the bell - you will be told that it is VIP only. The brothel madam will talk to you from the window and tell you to go to the back door.

Meet her there and show her your medallion (this is not related to this achievement but will advance your main quest) - she will ask you to do a mission for her, which is the mission you need to do for this achievement. The best way to solve this is to advance your main mission while you kill Maximo. Do as follows

For all the following - you need to observe the guards patterns as the mission is an instant fail if you get spotted. YOU CAN KNOCK OUT PEOPLE IF YOU CAN HIDE THE BODY - but this is not advised unless you absolutely must. I knocked out one other person than Maximo. It is advised to sneak/crouch at all times and Quicksave often as you most likely will be spotted a couple of times. The guards are not very observant and you can sneak right behind them if you crouch. On to the sneaking:

1: Enter through the back door and go left through the kitchen then up to the room with the guard standing by the right door towards the bar.

2: When he moves up, move into the bar area but take an immediate right and hide besides the stairs until the guards' patterns are good. Be aware that one guard moves up and down the stairs, wait until he is downstairs, the piano player is at his piano and the last guard is looking towards the entrance.

3: Sneak up the stairs and take a left into the sleeping quarters where we will advance the main mission. The prostitutes will not sound the alarm but there is a servant here that goes in and out of the room. Search the cabinets in the room for an important note that will advance the main story.

4: You now have two objectives 1: Kill Maximo and 2: Search the office. It is best to do this in that order. Move out of the sleeping quarters on the opposite side of where you entered (the left side looking up). There is a guard here that moves up and down the left side. Observe his movements to learn his pattern. When he moves towards the room where Maximo is, follow him closely. When he is nearing the end of his pattern, sneak into one of the rooms on the left side with a balcony.

5:NOTE - this is where I knocked out one of the guests that entered the room. I knocked her out on the balcony and left her there. She will be found before you exit the mission but the only thing that happens is that the guards go on alert for around 10 seconds. You can now overhear Maximo berating one of his prostitutes and when he sends her away and sits down in the chair you can move into the room (watching the guards patterns first) and knocking him out. You then need carry him back to the room with the balcony and throw him off. If you want to end the mission here you can do so, just jump off the balcony yourself and leave the map. HOWEVER, if you also want to advance the main story (which i heartily recommend) you need to pay a visit to the office on the same floor.

6:There is a guard that walks in and out of this office, but he is pretty easily avoided - you should know the guard patterns pretty well by now. Enter the office, search the cabinet for another important note, loot the chest in the room and sneak back to the room with the balcony again. Jump off an leave the map and you have both advanced the story and earned yourself 15G and some ingame Karma for killing Maximo.

One last note, there is an upgrade in the pigsty downstairs that you can pick up at any time during this mission (or later) should you desire to do so. Entry through the back door, then hang a right and another right. Watch out for the guards.