This achievement is won when you get to the next major town in the game 'Subway Town'. When you reach here you will find Teague in the subway bar on the ground level. In order to win this achievement you must beat her on the 'hard' difficulty (after starting the mini game you receive the choice of easy, medium or hard). You will Know you are on the correct difficulty because you will get 250 points to create your deck. I waited until I had completed the achievement to collect all the cards (just before the mission to Authority Prime) but for this solution you will require at least the cards mentioned below:
After taking to Google to find the solution to this I checked this Xbox sister site to this. Full credit for this solution needs to go to 'Witcher Bobmour' via the TrueAchievements website. I'm sure there is a tactic to this but basically, just use this deck and it appears to work every time!!
Select the following cards:
MUTANTS: J.K. Stiles, Large Mutant, Kraken, Giant Mutant
AUTHORITY: Power Supply, Enforcer, Shield Guard, Authority Mutant
SETTLERS: Captain Marshall, Valder, Loosum Hagar
SHROUDED CLAN: Shrouded Mini Gun
The game has an element of luck so if at first you don't succeed try again, but it popped first attempt for me!