You can leave this achievement for when you reach the second island; once there, you will go to meet with Sam. After you meet with Sam, you'll have to liberate "Harmanse Gas and Repair," which is east and south of Thurston Town, to unlock a side quest called "Father's Burden." After you accept the quest, you'll speak to an old gambler who wants you to win his money back from the mercenaries at the bar.
What makes this quest easy for "Poker Bully" is that because of the quest you can't lose. Go to the bar and bet all in until there's one guy left at the table, then press ESC to quit the table, then play again to reset the table. Do this until the achievement pops up.