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