Colt Canyon

A few tips to make this easier:

1. Turn in detailed HUD. There is a small incognito symbol in the bottom left, so you can be sure you weren't accidentally spotted
2. Unlock Mom by reaching level 1-2b in a looped run and her Light Bolt Rifle start by reaching the first boss area with her. She is incredibly difficult for enemies to spot, and the light rifle will 1 shot all early enemies
3. Ensure 1 shots on enemies by shooting them while they are unaware, this guarantees a critical hit (especially on higher health enemies this is necessary)
4. Unlock Camouflage early, I restarted a few a runs until the first prisoner had it
5. Turn off permadeath and get killed every time you are spotted to restart at your last save/beginning of the level
6. Enemies have a basic vision cone in front of them. You can tell the way they are facing by how their weapon is facing. The further to the side/back you are, the less you'll be detected. Obstacles and vegetation also help obscure you

The description doesn't say it, but you actually just can't be spotted by armed humans. Dogs and other animals can spot you and will not void the achievement. If you have a companion, they can also be spotted first, then you can shoot them, and it will also not void the achievement (although I found this to be way more trouble than just playing solo as Mom).

Otherwise, the main strategy I used was to mostly only move left and right, as you can see farther that way. I cleared enemies as I went, so I always could safely run left if I needed to avoid moving enemies. It is better to clear the enemies than try to avoid them as you'll end up accidentally walking into one.

If you're save scumming with permanent off, this is really just a matter of patience as you can keep restarting. The achievement unlocked for me as soon as I hit 3-1, not my partner, so it may also be currently bugged in our favor.