We Happy Few

I posted this initially as a comment on the other solution but figured it would be much better to make a separate solution for this.
After unlocking this achievement myself, and reading all over the internet, I came to the conclusion that you only need Arthur's playthrough (act 1) for this achievement.
Now, I will explain how I found out.
In my first playthrough, I decided to just pretty much slaughter everything that gets in my way if I can't stealth past it, and I even got the 100 kills achievement before I even finished the first act.
After finishing the game (all 3 acts) I restarted the game (using the "new game" option) and played through Arthur's act without killing anyone (keeping the murder stat at 0, non-lethal "kills" are okay, and I had plenty of those).
As soon as I finished the first act (and finished Arthur's story) I unlocked the achievement. It was during the load for the second act.
According to many sources, this is a common occurrence and while it might be a glitch (and it wouldn't be a stretch because this game has a lot of bugs) I still think it is necessary to let you people know that you don't have to go through all of it without any murders. Some parts (like the beginning of act 3) will truly test your patience and make you pull your hair out trying to do it non-lethally.

TL;DR
Might be a glitch, but you only need to finish Arthur's playthrough without any murders.
Personally, it worked for me (and others in the comments) by finishing the game killing freely and then replaying only Arthur's act, and upon completion of the first act, unlocking the achievement.

It's like the Achievement is already saying. Complete ENTIRE game with the 'Total murder' statistic at 0.
So NOT like the other solution that's saying only Arthur's playthrough. That's incorrect.

Non-lethal kills are allowed.

I've just received the 90G for this achievement by completing ENTIRE game. So all 3 playtroughs while keeping the 'Total murder' statistic at 0. You can keep track of it in the menu at 'notes'. On the bottom you will find statistics.

Tip: Use fist or takedown to do non-lethal kills. You can always figure out what's allowed by saving the game right before you are going to take someone down. So you can load it up again when you accidentally killed someone.

Addition to other guides already up.

IMPORTANT GLITCH NOTICE: Sometimes when trying to "smother a Npc in bed, you instead pick them up and upon setting them down says they are deceased. DO NOT PANIC! this is an odd glitch but it does not count as "Directly" Killing someone.

Also Important: you can check if you have accidentally killed a npc by pressing the "select/double boxes" button on your controller and pressing RT to get to the notes tab, and scrolling all the way down (faster with d-pad) to STATISTICS, and check your TOTAL MURDERS. (Non lethal kills are fine)

you NEED to go ALL 3 chapters without killing anyone, non lethal weapons and takedowns are safe to use.

GENERAL RULE : SAVE ALOT! you can have multiple save files use them! also each chapters character has their own set of save files, so don't worry about "saving save files" (puns ) for the other chapters!

NOTES


KEY RULE FISTS > anything except electric truncheon!

whenever possible SNEAK and use takedowns!
if you get caught run and hide and wait. repeat!
its not as hard as it sounds and this game rewards exploration via secret paths/vents passed enemies.


PERSONALLY i ONLY used: (Spoilers)


you can craft padded weapons but their not worth it. The Electric Truncheon is THE BEST non lethal weapon. at some point certain enemies carry them making it easy to keep a few on hand.

This is a disclaimer, not a guide. As of March 17th 2021 I can confirm that at least for Xbox One you only have to complete Arthur's playthrough without directly murdering anyone. I attempted to do a three person no murder playthrough but found it's too difficult with the lack of early takedowns for Sally and the amped up aggression against Ollie; I did directly murder people in those two playthroughs but Arthur's remained at zero. At the end of the game on my very first playthrough I was granted the saint achievement.