Is it possible to achieve the "Unachievable" achievement in "The Stanley Parable"?

Yes it is... But it depends on what you define as legitimate :) Copied from this Youtube video:

Ok, I have no idea that this is the intended way to get this achievement, but it works.
Here is how:

1. Close the game!
2. Edit your config file, it is located in your Steam folder. For example: D:SteamSteamAppscommonThe Stanley Parablethestanleyparablecfgconfig.cfg just open it with a text editor
3. Add this line to the file (in a new row): bind "x" "~;_u"
4. Save the file then right-click it and chose properties.
5. Check the attribute "Read-only" and save this change. This will make sure that the game won't overwrite your new key bind
6. Open the game and start a new game
7. Hit the "x" key
8. Wait a few seconds
9. Achievement Unlocked!

Thanks to the Steam user AoM, Phone_Answerer and nairolf for this method :)

Technical stuff:

If you try to enter _u into the console, you'll get a strange error:

Hey don't you even try

Also, if you try to enter ~;_u in the console, you'll notice that the ~ is a forbidden char in the console. That is the reason why you need to make a key bind which executes this command.

Someone on the Steam forums also decompiled the game and found this code:

if ( !sub_104B22A0(v26, "map1", 4)
  && RandomInt(1, 15) == 8
  && v46
  && *LODWORD(dword_107E1B28) > (float)(*(float *)&dword_107E1898 + 20.0) )
{
  v27 = *(_DWORD *)(sub_1027BBA0() + 28);
  v28 = *(_DWORD *)dword_107E1B30;
  v41 = (int)"_un";
  v40 = v27;
  v39 = dword_107E1B30;
  (*(void (__cdecl **)(int, int, char[4]))(v28 + 156))(dword_107E1B30, v27, "_un");
}

So as you can see there is some kind of randomness involved && (RandomInt(1, 15) == 8)

Developer comments

The developer also commented on this method:

Gran PC:

I don't really approve of reverse engineering the game and then divulging the way :/

He also posted this:

Gran PC:

The fun part of the achievement was having people try to work out connections really. I updated the code of the achievement every patch to account for whatever you guys discovered. Oh well, no fun allowed for developers I guess.

and this:

Gran PC

It's no fun if everyone knows it's almost random!

In one patch I made it so quicksave & quickload would grant it, and in the next patch I made it so it was impossible to get through quickload. It was hilarious to watch people like the original poster raging :P

You can find these comments (and more) here: http://steamcommunity.com/app/221910/discussions/0/792924412213692581/#p54

I also wrote a blog article about this. It's a bit more detailed for anyone who's interested: http://www.themutegamer.com/guide/the-stanley-parable/unachievable-achievement/