This is story-related and hard to miss (the narrator will tell you about the achievement), but...!!
The game will reset (delete) the achievement if you keep playing after unlocking it!
To keep the achievement - as soon as it unlocks, hit ESC, quit to the main menu and exit the game!
Note that re-starting the game will reset the achievement. If you want to experience the full demo, just play it normally until the end and then play it again up to the achievement. (Which only takes a couple of minutes if you rush through.)
The Steam overlay / task manager switching method mentioned in other guides is not necessary - and actually doesn't work for everyone. (Including myself when I tried it.)