When you perform a Covert kill, you will see the word appear on the screen just as it does when you get a Combo kill (see Combo kill posting for a full explanation). There are very few places in Wasteland Legends to get Covert kills and getting a Covert kill is much harder obtain than getting a Combo kill. Also, due to the large number of kills (15) getting the Covert kill emblem requires a lot of time. The Wasteland Legends mission I used to get the Covert kills was in "Life in Prison". There may be other Wasteland Legends missions to get Covert kills, such as "Season 1: Pilot" or "Extermination", but in order to get credit for your kills you must finish the mission. If you quit a mission before completion or both you and your partner get killed before completion, the kills or collectables you may have obtained in a mission are lost. "Season 1: Pilot" and "Extermination" are the hardest missions to complete by far, even with the difficulty set to Normal and that is the reason I choose "Life in Prison". There are three soldiers in this mission, located in different locations, that have their backs to you. You must sneak up on them quickly and use a Wingstick to kill them. This is very hard to do because you must hit the soldier exactly in the right spot to get the Covert kill. When done correctly you will see the words "Headshot" and "Covert" appear on the screen.
You can only get (at least that is all I could ever get) 3 Covert kills per "Life in Prison" mission play. That means that at a minimum, you must play the mission 5 times, getting 3 Covert kills per mission, in order to obtain the required 15 Covert kills. If someone knows of a better mission or place to get Covert kills, then hopefully they will reply to this post.