To get this achievement, you first must have researched the "Arc Thrower". After researching it, build at least one in engineering. Now the Arc Thrower is a pretty close range weapon, so I highly recommend using support characters with smoke grenades to close that gap safely.
Now its not a guarantee that you will stun the alien, so i reccommend having either 2 people go in with Arc Throwers at the same time, or have another soldier ready to kill him if it fails, and try again with the next mission.
You'll probably get this achievement before you level up a sniper high enough to take the perk, but capturing a live alien can be made easier if a sniper can first make a 'disabling shot'. The alien losses any reaction shot from overwatch and will likely spend their next turn reloading their weapon to repair it. So you can either get in a second round to retry the arc thrower attempt if necessary; or else dash to close the distance and stun them next round