The story of this achievement is that at release, you'd need to meet some unknown criteria and have a bit of luck (like a 1 in 15 chance) to get it. However, as people were figuring it out, the developer would patch the game to change the criteria.

The descent into madness of both the players and the developer is well documented in a nice blogpost[www.themutegamer.com] and a huge thread on the forums.

Players started to reverse engineer the game to figure the rules out. They found some shady workarounds by editing the game files, which is explained in many guides. Isn't that a bit cheating though?

https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=1137924364

As far as I know, it is currently unknown what the developer intended way to get the achievement is in the latest version.

However, from reading the forum thread, we can figure out that at least at some point the achievement could be gotten from loading a saved game. This user got their achievement on 19 Oct, 2013 @ 10:21pm CEST.

According to steamdb's history[steamdb.info], they must have been playing depot 1072861593784438029 at the time.

You can get Steam to download that version and get the achievement using the loading method. Isn't that less cheating?

The first steps are based on https://www.reddit.com/r/Steam/comments/611h5e/guide_how_to_download_older_versions_of_a_game_on/.

1. Open the Steam console (steam://nav/console). Probably easiest to do via the reddit link.
   
2. Enter: download_depot 221910 221911 1072861593784438029
   
3. Wait for the download to finish (it'll say where it ended up in the console)
   
4. Go to the game installation and move all the files out of there.
   
5. Move the just downloaded files into the game location
   
6. Start the Stanley Parable from Steam

Now you're running the old version. I did this to get the achievement.

1. Start the game
   
2. Make a save after the intro
   
3. Go back to main menu
   
4. Load the save
   
5. Walk around a bit (<30 seconds)
   
6. Repeat steps 3-5 until the achievement pops (it took be about 20 tries, your mileage may vary)

(After this you can move the original files back or tell Steam to verify the download to get back to the latest version.)