This is a very easy achievement if you have the right cards (refer to this to obtain them
The key to winning is in preparation, first by getting the right cards and second by building an appropriate deck. Now you have about 250 points to work with meaning you're going to have to put up a lot of cards, but just because you have this leeway doesn't mean you should just put your toughest cards in your hand for there are many factors to consider.
1st you want to look at is cards that boost certain other cards (ex: jk stiles +2 damage to all mutant cards) you're going to want to have at least one of these coupled with the strongest cards it buffs, for this challenge you can't afford to have weaklings (ex: don't put in a dagger thrower for this).
2nd look at whether or not a card is ranged, you are going to want to have as many ranged cards as possible because they can attack any card on the field and therefore you can triple team certain cards. The only downside to this is that you can counter act this by playing a vehicle (all ranged have to attack vehicles), but Teague will almost certainly play only play one vehicle (12hp dropship) but if you build your deck right it won't last more than a round or two.
3rd since you have so much leeway put multiple groups of cards in your deck so you're more likely to have a buffer and one of it's correspondents on the field (ex I had mutants, authority, and settlers).
Luck does play a pretty decent role in the game (more so in early games), but for the final challenge it's going to ultimately depend on the card's you have accumulated and how well you built your deck. Teague is more than likely going to use Authority and Mutant cards, but she also has a lot of grenades, mines, vehicles, and healers so they're not too much of a challenge. If you have gotten all the cards up to the point you reach the bar you won't have all of them but you'll have more than enough to beat her, just put together a deck comprised of three card groups with only their toughest ranged characters/buffers and no vehicles, healers, or explosives and you should be fine.
If all that isn't enough just put in the deck I used and use common sense to win the game.
MUTANTS: J.K. Stiles, Large Mutant, Kraken, Giant Mutant
AUTHORITY: Power Supply, Enforcer, Shielded Enforcer, Authority Mutant
SETTLERS: Captain Marshall, Valder, Lousy Hagar
Shrouded Mini Gun to fill up the last spot
hope this helps