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