GYLT

So this achievement can be tricky. Way back when this launched exclusively on Google Stadia it was actually completely broken and even after they did a patch for it I did a run where I thought I didn't kill anything but still had to do another run after to unlock it. Luckily playing it again on Xbox and Steam I think my strict guidelines are the best way to guarantee you unlock this as I did it first try on both.
I plan to add a video in the next couple of days but in the meantime I have a write up below.

1. Play this in one sitting
You're allowed to quit out back to the main menu (say if you accidently kill something) but just keep the game open. A speedrun should take you less than an hour and a half. So do this when you have the time.

2. Avoid every possible enemy encounter
A few you can't avoid.
-On your way to the arcade you pick up this flashbang like upgrade for your flashlight and get jumped by three enemies, either try to flash them and run or just run
-You encounter invisible exploding enemies at two points during the story
a. The first time is unavoidable at the theater after you do the little puzzle with the vending machine and kill the eyeball, simply hug the wall after exiting the locked door and watch the feet prints on the ground and circle around them to quickly run up the stairs
b. Once you reach the gym if you just hug the left wall they shouldn't come at you an once you solve the timed electricity puzzle they'll spawn out and regular enemies spawn in
-After you've entered the final mine area of the game everything is easily avoidable but you'll eventually come to a part (after you've lost your flashlight) where you come to an area with a small bit of fire on your left and a doll enemy on your right. Get rid of the fire but then you're stuck with a fork of a doll on the left and nothing on the right. If you go right you'll alert the other doll so instead just walk up the doll in front of you, freeze it and then quickly run to the gate with fire and put it out so you can crouch under it
-During the four boss fights it's okay to get spotted

Outside of the above mentioned things, if I ever saw an enemies arrow turn red I would quit out and continue from my last checkpoint. It might be overkill but I'd rather be safe than sorry and have to do a entire run again.
So with all normal enemies besides the invisible ones remember your ABC's.
A - Always
B - Be
C - Crouching
Always be crouching!

3. Do no worry about collectibles or other miscellaneous achievements
I highly suggest you enjoy the game and get your collectibles in your first playthrough and you save this no kill run for a second run all by itself. That way you'll also have familiarity with where to go and know what enemies will be where and so you can avoid them more easily. You can also always mop up collectibles after the speedrun since you get an option to spawn back at the school and will have everything unlocked.

This achievement unlike the story ending ones will have a short delay and will pop during the credits.
Good luck!