This isn't quite as difficult as it sounds. Ada's section is quite short and there was only one tricky part as far as I was concerned.
In my run through, I avoided the use of any item whatsoever except the EMF. I did however use a typewriter which won't void the achievement in normal difficulty.
You start off near a ladder. Interact with it for a short cut scene and a brief description of the EMF which is selectable via hotkey by pressing
. Destroy the fan and move through the next tunnel.
Before dropping down you can unlock the door. Do so as there is a zombie in the room, which although doesn't present a huge problem, it does make sense to not try and open the door while you're in the room with him.
Move through the newly unlocked door. Run across the catwalk and down some stairs to the right. This is where I found it slightly more difficult than the rest of it, but shouldn't be too bad if you're prepared. There is a lift, and you will need to activate it by hacking a terminal on the far left side of the room. Keep track of the blue wires by occasionally scanning with the EMF but make sure to sprint through this section as by now you've attracted some zombies. There is a crate by the terminal and you should use this to lure around 3 of the zombies to the far side so that you can slip out of the other. I was still bitten here, but don't sweat if it happens to you, the rest of Ada's section is cake.
Go up in the elevator you've just activated. Now you're going to have to deal with the tyrant but he didn't even get close to me, so you should be fine. Go to the end of the corridor, hack the terminal to the right of the door and open the door with the switch. The tyrant is coming for you now, so be quick go through the door and quickly turn around and hack the switch above the door you came through. You will have just enough time to hack the fan and jump through it with
before he can get you.
Follow the corridor round. You should see a typewriter. When you do save your game. There is a Mr Raccoon here so shoot it if you need it, then simply reload. The rest of Ada's section will only require the use of the EMF so you shouldn't have any reason to use any items. Once the final cut scene has played out, the achievement will pop.