When you go the 1st floor, interact with the tennant in apartment 113 to get the code for apartment 114, just to the left down the hall. Once inside, pull back the curtain on the left and enter the door on the left. Once inside, scan the woman sitting down with
and find you can interact with and enter her mind/dream.
You'll go through a fairly linear dream sequence type of area where you will walk through a long hallway then go through a virtual canyon with wind pushing you back every so often. You can either take cover to stop from being pushed back, or just sprint and you hardly get pushed back at all. There are some switches along the way that you need to press or slide to open up the way.
When you finally reach the woman you enter a conversation with her. As far as I know, what you say doesn't matter, but you will be kicked out of the dream area and back into the room you originally found her in.
Now, to the left of the woman is a computer that, once you open it, you can scroll down to the programs and just under the "withfireandsword" game is a program called cephalus. Choose whichever choice you feel like and the achievement will pop.
EDIT: According to TheOnlyMatto, opening the computer after the whole sequence might crash the game and he said leaving the room for an autosave and going back in to interact with the computer won't make it crash.