Here is the full list of all 20 Poker Night at the Inventory achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Check a pat hand.
Knock out The Heavy after he's bought in with his special item.
Knock out Tycho after he's bought in with his special item.
Win consecutive all-ins.
Win a showdown with just a high card.
Knock out Max after he's bought in with his special item.
Knock out Strong Bad after he's bought in with his special item.
Win a pot with two or more opponents when you are all in.
Win a hand with Four of a Kind.
Win a full game.
Win a hand with a Flush.
Win 12 or more hands.
Win a showdown where you and the opponent have same hand (pair or better) and you have a better kicker.
Win three straight pots.
Win a hand with a Straight.
Win a hand with a 6 card and a 9 card of any suit.
Win a game on hard.
Win a hand with a Straight Flush.
Win a hand with a Full House.
Win a hand when you have three of a kind comprised of three kings (of any suit).