You find the arcade machine in the ACTIVE INVESTIGATIONS ROOM, after you've first encountered Hartman. The machine seems to have two modes, CROWD CONTROL and DEADLINE.
The description says, you need to play an arcade game.... but it looks like you actually have to complete one game successfully.
I got it on Crowd Control (surviving enemy hordes).
If you're struggling (and you don't mind feeling like you're cheating), just turn on assist mode. It will be a breeze.
Once you complete a game, you unlock the achievement and the other arcade machine lights up as well with five new game modes!