From Old Willey Pete on the Xbox Achievements page and confirmed by me:
This achievement is extremely easy, you just need to progress until you reach the second island. Once there in Thurston Town, there is a sidequest called Father's Burden. Accept the quest and follow the markers, you'll speak to an old gambler who wants you to win his money back from the mercenaries at the bar.
You pretty much can't lose because of the quest so once the game starts go All In. You should win the hand, once you win exit the game and then sit back down and play another round. You should have the achievement in two games total time of about 3 minutes.
EDIT: FishHeadN pointed out you can just play that poker game to it's conclusion and you will win $1500. So there you go, you don't even have to exit the game and play again unless you want to farm money (which you can do, rather easily.) Otherwise, just always go All In and you'll win about 75% of the hands and the game ends when you have won $1500.
EDIT: Badtriangle has pointed out that you have to take out a nearby outpost called Harmanse Gas and Repair which is east and south of Thurston Town along the coast road. Precisely at X: 606.3 Y: 489.2