When you enter the Casino, go up the staircase on the right to get to the slot machines. Upon entry to the room, the Poker Slots are at the back of the room.
In order to give up Three of a Kind, you'll be required to produce 3 of the same card (7,7,7 for example) on your first pull. The slot machine will automatically "Hold" these cards by pressing for you on these cards.
Now, before you pull again, make sure the light below these cards is not lit. Press while selecting these cards to ensure you will give them up. Now pull the handle and hope you get a winning hand to unlock this achievement.