You will earn this achievement by not killing any haunted in Chapter 2 not counting Connolly. This is fairly simple.
1) When you get to the sneak kill tutorial, DO NOT sneak kill the haunted! Just wack him, lure him away from the door, run in and out the window.
2) The next section you can distract the haunted with a bottle or just run to the next section. A checkpoint will activate when you get there so you could just load the checkpoint and those hunted wont be there. It shouldn't be necessary as you want to be seen in the next section anyways.
3) So now you are in the area with a big fire and a haunted just sitting in front of it. What you want to do here is make your way to the gate and lure all the haunted to the start of this section. Be aware some haunted will not appear until you use the gate. A Sebastian with fully upgraded sprint will make this a lot easier. Once they are at the far end, run back to the gate and open it as fast as you can.
4) Once you pass through the gate, run to the bridge and cross it to end the level. Do not worry about the haunted here. As long as you can out run them you are golden. If you cant you will need to take the scenic route to the left immediately past the gate and around until you are forced towards the bridge. From there you will be able to run across the bridge before the haunted can catch you.