All mini games and mini game locations become available during Chapter 2, after a mandatory game of Poker. An important note is that some game instances are in temporary locations, and some are permanent. The below listed are
permanent.
Playing 1 game of each will unlock the achievement.
Poker: Mandatory as part of the story; also in the main Saloon in
Valentine.
Five Finger Fillet: Inside of the smaller Saloon in the town of
Valentine.
Dominoes: At the
Emerald Station (accessible by train).
Blackjack: The town of
Rhodes (accessible by train), second story of the Saloon.