Here is the full list of all 20 Premium Pool achievements.
Play 1000 online matches
Play 500 matches in the tournament mode
Collect 1,000,000 coins
Play 100 matches in the tournament mode
Own 10 cues
Win a tournament without losing a match
Achieve level 10 in a tournament
Play a tournament and claim rewards
Win a match when opponent pockets 8 ball prematurely
Play in 5 different locations
Win 10 matches in a row
Play 100 online matches
Win 5 online matches in a row
Win a game by pocketing all balls in a row in 8 Ball
Get 6 hit streak
Beat opponent in a match without them scoring
Pocket two balls in one shot
Get 7 hit streak
Win your first online match
Collect 10 million coins