This is story related and cannot be missed. Before attempting this you need to research the ‘Arc Thrower’ via the lab. (Researching the arc thrower is story related and will be available after researching Xeno-Biology) One the research is complete, construct it in engineering and outfit it on a soldier for the next mission.
Once you are in a mission you need to be close to an alien, (3 or 4 spaces from them and have a clear LOS.) Unless an alien approaches you, you will need to move close on your first turn, then use the arc thrower on your second turn. Press to select the arc thrower and fire. You only get one shot and there is still a chance you will miss so either reload a save, or have a second soldier standing by to try again if the shot misses. Otherwise the alien will go down and the achievement will unlock.