I did this achievement and Lethal Shot (Finish a Mission with 90% or more Accuracy) at the same time. I first complete the game so I had every upgrade but I'm pretty sure you can do this achievement right at the beginning. First, make sure the difficulty is set to Easy (When the mission begin, press start and change it under game options)
Kill the first guy you see with a headshot, using your Sniper , then you can proceed the level using Only melee and using grenades (They doesn't affect accuracy). You will come near the end of the level with a giant turret to destroy 2 ships. Make sure you shoot slowly because those counts for the accuracy. You can even take your time, those 2 ships are really bad.
You should unlock both achievements at the end of the level.