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