This is a story-based mission that takes place on Kadara, so you'll have to progress enough in the main story to have access to the planet.
This mission takes place after you do a few missions for Reyes Vidal. Once those are complete (to include attending a party with Reyes that Sloane Kelly throws), you will get a message from her that she wants to speak to you at the Outcast HQ. She will be there, alone. She will inform you that The Charlatan (the leader of The Collective, the opponents of the Outcasts) has had her second-in-command, Kaetus, beaten up. She has a message that the Charlatan wants to meet her in Draulir, a location in Haarfel on Kadara, and she needs your help because she thinks it may be a trap. She will ask you to meet her at the designated location and you'll be given a quest marker there. When you get to the marker, she will be waiting for you outside a cave.
Before you start the conversation with her, make a save, because the "interrupt" choice(s) you will make soon will determine who will be in charge of Kadara after the meeting, because it is indeed a trap, in addition to the earning of the achievement.
Walk up to Sloane, and you will get a cutscene. You will find out that Reyes Vidal is actually the Charlatan, and he has attempted to lure Sloane to the cave with the intent to kill her. During the conversation and the start of the one-on-one duel (hence the name of the mission), you will get the flash of a sniper scope and you'll get an interrupt chance to save Sloane's life. There are two interrupt possibilities here:
1. If you allow Sloane to be killed, the mission will continue with a quest to meet Reyes in Tartarus, the nightclub in the Kadara Slums. After a short conversation, the output will be made available to the Initiative, the two will shake hands, and the achievement will pop. If you want Reyes in charge for the rest of the game, you can continue from here. If you want Sloane in charge, reload the save, and proceed with the second choice.
2. If you take the interrupt to save her (no achievement), there will be a continuation of the cutscene where Reyes attempts to escape by shuttle. You will get a second interrupt here to shoot him before he does (the shot does not kill him, and he escapes). The mission will continue, with a new step to talk to Sloane at Outcast HQ. Here, she will essentially extort a cut of the revenues from the outpost in exchange for allowing it to be there, but you get the outpost in the end.
No matter who you finally decide to be in charge of Kadara after the mission, they will be with you for the final mission of the game.