Ok so the easiest way to do this I found by accident.
You need 2 players for this method. What you want to do is have the host get a headshot, then player 2 runs through the game killing everyone else any way he or she wishes. You need to leave 1 enemy left, you(player2) then go to the dashboard, close Warframe and restart it. It will ask you once logged back in if you wish to reconnect to your lost party, say yes.
Once you re-join, headshot the last enemy...ignore Vor if he's there and run to extract. Since you "disconnected"...all enemies you killed no longer appear to count as the stats are whiped. So you and the host should only have 1 kill each and both are headshots.
Tested this, worked for me and my brother.
Note. I believe this needs to be done twice...I don't think the Host will get the achievement because to him the kills still count but they wont for the returning player because to him he's starting fresh.
Added tips and comments.
-Need 2 people
-Host doesn't get achievement
-Use Loki to stay invisible to make this really really easy
-Energy restores are useful to keep your energy up to stay cloaked or use Loki prime to get energy from death orbs.
-While you are player 2(not the host) make sure to destroy traps on your way through so the one guy you leave alive doesn't decide to take a stroll and walk into a death orb laser.
-Staying cloaked helps you keep away from annoying Corrupted Vor.
-Bring a good/strong headshot weapon and check after your kill to make sure it registered as this game seems to have issues with registering headshots from time to time.
-Obviously don't leave your 1 target left something like an Ancient, MOA, or Drone. Lancers and Corpus Crewman are the weakest and easier to headshot.
Goodluck and let me know if this is not working for you.