This one was the last one I got, and the most painful for me to earn (took several hours of work before finding the below).
The Doppelganger, the visitor that looks exactly like you, appears at about the sixth 'Eye' level, where you must hide and avoid the visitors. This will be the level right before the 'Giant' visitor is seen during the house levels (find the clock, exit to the woods, get back in the house). At later levels, other visitors are more prone to show up, so it's probably best to keep retrying this level. Otherwise, you might have to put in another hour or so getting back to level 6.
In order to get this achievement, you have to make your doppelganger fade away. I had extreme trouble doing this, as fixing the light while he was, or pressing up while he was walking did not seem to work for me. What did, oddly enough, was to catch him in the Breach room when he first appeared. He stays in place for a little, before he is teleported elsewhere in the house. I stood on top of him, and my character started to fade away, leaving the doppelganger. I then got the achievement, and could continue on with the game.