To unlock this achievement, you will have to play on the slot machines, which you can find in the Jackpot area after you gave Sarah the plans of Firestone. There is no easy way to obtain this achievement and it's all luck so it could be faster for one person than another. Allow me to explain me my tactics, it helped me gain this achievement rather quick:
After the first dealing, check what cards you have. If you got 2 of the same kind (example 2 sixes), hold them by marking them and pressing X. If you got 3 of the same kind (example 3 sixes); hold them as well since you only need one more. If you got 2 pair, hold all four cards and deal again. If one of the numbers pop up (example: 2 fives and 3 sixes), unhold the 2 fives and deal again and see if you get a card of the same kind (in this example, another six). If you don't get another six, a 'three of a kind' will always give you 3 times the money you have betted (example: if you betted $5, you will earn $15).
This way, you will still earn money (you will loose some since the slot machine can be kinda tricky) and luckily, you'll get your achievement as fast as I did (I did around 20 tries betting $15).
Have a good day!
It is not required to get 4 aces. I unlocked my achievement with 4 Jacks (or should I say mutants