Here is the full list of all 21 Premium Pool Arena trophies - there are 21 bronze.
Win your first single player game
Pocket 100 balls
Win a game when the opponent pockets the 8-ball prematurely
Pocket 6 balls in a row
Pocket two target balls with one shot
Win a game without committing a foul
Pocket 7 balls in a row
Play a tournament until the end
Play 100 games
Beat an opponent without them pocketing any balls
Win 10 games without committing a foul
Pocket 1,000 balls
Own 10 cues
Play 100 games in Tournament mode
Win 100 games without committing a foul
Play 1,000 games
Win 10 tournaments
Win the hardcore tournament
Play 500 games in Tournament mode
Pocket 10,000 balls
Win a game by pocketing all balls in a row