Figured I'd post a little something even though this achievement is pretty simple.
Best way that I've found to get this early on is on the Earth> Pacific mission.
Easiest done solo. *Or if you have a friend or group of friends who will not go for kills, it can also be done. Plus then they can also revive you if downed.
Just (As in any mission if you want more kills) let the enemy activate alarms so that they come looking for you.
There's no time limit so take as long as you need until hitting 100.
The achievement will unlock as soon as the "100 Kills in a Single Mission" Challenge update pops up.
At the end of the mission I had 111, and it was probably still possible to go further.
Hope this helps anyone who's wondering about it.
**After some kills(Maybe 10-20) the area you are in will deplete of enemies. Don't fret, just move to another part of the map, without disabling the alarm. That area will have more enemies, and after that area you will have to move again, either a new room or the previous one because enemies should be respawning depending on how long you took.