For this one you need to kill all enemies on every Nightfall level.
You may find full video guides online but it will probably be easier and faster to deal with it on your own.
Main tip is to go loud.
Take kills as they come and do not use shadow kills. You will want corpses to be found as when this happens and the alarm is raised, a '!' icon will appear for each remaining enemy in the area (which helps making sure you've completely cleared the area).
When you think you're done, run a couple of times around the area whistling as much as you can (
). If you missed someone, a '?' sign will show up if they can hear the whistle.
On Chapter 2, don't worry too much about killing enemies whilst you follow the messenger. Once you reach the elevator you will be able to open each light gates and backtrack to the start of the level. Just make sure you don't take the elevator!
On Chapter 4, in the final area which is a timed section, you do not need to go through the locked door on the left (there are no enemies there). You do need however to go through the house locked by a light wall on the right, as there are a few enemies inside (5 or 6). To unlock the house (in case you attempt this on your first run and don't know how) you need to hit the switch in the cave underneath the house.
One last piece of info that may help you if you want to try to keep counts, are the number of enemies I had during my run for each level on Easy mode (may be more on harder difficulties):
Level 1: 53
Level 2: 73
Level 3: 61
Level 4: 50