A stealth kill is any kill on an unaware enemy.
Edit: You now recieve a XP bonus for some, not all stealth kills. This is marked on the upper right as a 30 second boost.
A stealth Execution can be done on most enemies. Walk or run up behind one. A pop-up will tell you to press
. Your Tenno will perform a special blade strike for a guaranteed Stealth Kill. Using a melee stealth kill might alert nearby enemies.
If you have a bow, Ranged Stealth kills become possible on most enemies. Find an unaware enemy, fully charge the bow, and aim for the head. Ranged stealth kills rarely alert enemies. However, you might not deal enough damage for a kill. If you hit an enemy and don't kill him, that enemy will become aware of you. The Mercury-Terminus-Exterminate mission is a good one to get bow stealth kills.
Missions against Corpus give a great opportunity for stealth kills with any ranged weapon. Throughout each mission, there will be security cameras on the ceiling. If you kill one while it has blue lights on, that will sometimes count as a stealth kill. Sometimes, the lights flash to red before it dies, and that won't count. I got about 3/4 times counting as stealth kills. Try it on Venus-Cytherean-Exterminate.
Edit: An update might have made this stop working, please let me know if the achievement counter advances or not for you.
If you have the starter warframe, Excalibur,
and the mod card Radial Blind, you might get stealth kills with that ability. Get your warframe up to about rank 6,
and equip the mod card. In a mission, press
to choose Radial Blind, and
to use the ability when you have at least 50 energy. Opponents affected by Radial Blind are temporarily unaware of you. Kill them quickly for a stealth kill, but the window is brief.
EDIT: An update changed how you receive Warframe abilities. You automatically receive the power at some level now, Once you have the power "Radial Blind," use the steps above.
Edit2: Energy cost reduction and duration extending mods will make this more effective.
It's hard for me to keep track of changes on MMOs, so please alert me if one of these methods stops working.
Also, whenever possible, try to get stealth kills while on a zipline so you can earn progress on this achievement: