Dishonored Definitive Edition

The first possible place to "assassinate an assassin" is Mission 3: The Golden Cat. They appear by Slackjaw's area.
If you see one of them first, simply sneak up behind them and stab them in the back.
If one of them see you first, blink over their head and quickly stab them in the back (how I got the achievement).


The simpler way to get this achievement is to just wait until you get to the Flooded District later in the game. There are plenty of assassins everywhere, and you just have to assassinate/stealth kill one of them.

The earliest you can achieve this in Mission 03: House of Pleasure. Once you have talked to Slackjaw for the first time, he will tell you to go to Galvani's house. Once you exit the distillery and get back onto the streets of Dunwall, you will face an intersection where you can either go forward or right. Swivel your head to the right hand side and blink up to some pipes along the building. You will notice that there are three assassins camping out and tryna peep you. Just sneak up behind one undetected and press left mouse button. Cheevo popped.

This can also be accomplished in Mission 07: The Flooded District. There's a ton of assassins in this level, so I'll let you figure out a way to sneak up on one and passionate them. Shouldn't be too hard with things like stop time.