For those without a Loki or Ivara and maybe not even having level 30 weapons there is a pretty straightforward way to get this done.
If you have a sentinel or kubrow, leave them behind.
I used an Excalibur and chose to go to Earth to find a nice low level mission with infinite enemies, or in other words, any mission that is not an exterminate. I don't recommend a defense mission for this as there is an extremely small map and even if you are on a line and they don't see you, they are in attack mode and chances of getting a stealth kill are much lower. There are several rooms that spawn on Earth in the low level sabotage mission on Mariana that can make this very simple.
Find a room with a zip line and hop on up. It didn't matter if I cleared that room first or not as I found that there would be at least a couple more that would randomly wander into that room. If I didn't see any enemies for about a minute I moved on to another room. On my second run I had a room where there were entrances on both ends and a zip line in the middle. This particular room is also the tile that you defend your kubrow when you first get it in the "Howl of the Kubrow" quest. In less than 30 minutes total I had my achievement. Of course this can vary depending on how the tiles fall for you.
A few tips are to always attempt a headshot. I know, head shots on Grineer are hit and miss as far as getting credit for them, but even if you don't one shot them and they become aware of you, there will usually only be the one or two enemies and after you take care of them the next few in the room will be unaware of your presence.
Don't sit on a line for two forevers waiting for one to wander in, if you don't get one in a minute or so move on.
There are several zip lines on the low level Earth missions to work with so even if you don't get all of your kills on one line you may have several opportunities on the same mission to get it done. I do believe that Earth offers the highest amount of zip lines to work with. If there is a place with more lines then chances are the enemies are higher level and have a better chance of surviving a headshot.
And if you get two enemies walking in at the same time try to take out the second one first. If you take out the first one then the second usually becomes aware of you and you tend to not get a stealth kill for the second.
Hope this helps. Happy hunting.