Here is the full list of all 31 Governor of Poker 3 achievements.
Reach level 20
Play a sit n go poker game
Unlock 10 saloons
Win 100 hands in any poker game type
Win a hand with a straight
Win a hand with fullhouse
Win 50 hands in any poker game type
Do a rebuy in any poker game
Reach level 10
Win a hand with three of a kind
Win a hand with a highcard
Unlock 5 saloons
Win 10 hands in any poker game type
Win a hand with a flush
Reach level 3
Win a hand with two pair
Win 500 hands in any poker game type
Win 1000 hands in any poker game type
Win 2000 hands in any poker game type
Win 5000 hands in any poker game type
Win 10000 hands in any poker game type
Win 50000 hands in any poker game type
Reach level 30
Reach level 40
Reach level 50
Reach level 60
Win a badge in any sit n go tournament
Unlock 15 saloons
Win a hand with four of a kind
Win a hand with a straight flush
Win a hand with a royal flush