This is a pretty simple achievement. Unless you are reckless, you will most likely get this in the second mission. Otherwise, when you get an option to choose an "Alien Abduction" mission, look for one rated "easy". There should only be 2-4 aliens on the map, so just proceed carefully, always staying in cover, and you should be relatively safe.
If you are still having a problem getting the achievement, just save after each turn and reload whenever someone gets killed.