At the beginning of Act I: "Of All the Gin Joints...", when you are
supposed to go to the "Ghost Note" club, after you reach the club, you
will see a loading screen and short cutscene. Before entering the club,
go left, and look for a building with a red neon sign and white text
that says "24h Dirty 24h". Walk up to the door to get the "Not That Kind
Of Game!" trophy. You can also do this after leaving the "Ghost Note" club.