You'll need a guy with beholder sleeper agent perk. You're going to need to hire lots of guys with hidden perks, hoping to get this one. I've read that hard difficulty increases the chance of getting one, but honestly didn't notice it. They come by sometimes and you'll get one eventually.
There's also a possibility to get the perk on the story related recruit connected to the Leonidas programme, if I remember correctly, but it's deep into the game, so probably not worth the wait.
If you get one of the sleeper agents you have to go to a tactical mission, break infiltration (shoot someone with an unsilenced weapon, basically) and - what made me overthink the achievement - wait a turn. The agent doesn't change sides until the next turn, so don't panic :)
Once he does though, you get the shiny, shiny cheevo.
(the mason gambit doesn't work on that one, neither does trigger phrase, tried those out. It seems that it's you that needs to be betrayed, not the Beholder. I've read a rumour that the combination of the two works for PC and PS4, but didn't try it on xb)