Here is the full list of all 43 Billiards of the Round Table (BRT) achievements.
Complete all Beginner levels in Magnet mode with 3 stars
Complete all Classic levels in Magnet mode with 3 stars
Complete all Ace levels in Magnet mode with 3 stars
Complete all Master levels in Magnet mode with 3 stars
Unlock the Champion cue ball
Achieve a score of 22000 or more in Arcade mode
Achieve a rating of 100 stars or more in Magnet mode
Achieve a score of 8000 or more in Spin mode
Complete the Arcade mode tutorial
Complete the Magnet mode tutorial
Complete the Spin mode tutorial
Complete all tutorials
Link 6 marbles together in Magnet mode
Pocket 3 balls with a ricochet in a single Spin game
Use 10 extra balls in a single session on a Magnet level
Win a game in Spin mode without using the Windup button
Send a ball flying outside the table in Spin mode
Follow proto and take 10 to 12 shots with a pink cue ball in Arcade Mode. Try it out!
Achieve a 14-ball streak in Arcade mode before the timer runs out
Reach level 5 in Arcade mode
Reach level 10 in Arcade mode
Reach level 15 in Arcade mode
Reach level 20 in Arcade mode
Clear 10 Magnet levels without polarity-switching shots
Clear 10 Magnet levels with polarity-switching shots only
Clear 15 levels with 3 stars in Magnet mode
Survive 10 ejections in Arcade mode
Achieve victory in Arcade mode with exactly 2.5 cue balls remaining
Unlock 10 cue balls
Unlock 20 cue balls
Unlock 30 cue balls
Unlock 40 cue balls
Achieve a 9-ball streak in Spin mode
Hit the rubber at the back of Spin table pockets six times in a single game
Reach level 5 in Spin mode
Reach level 10 in Spin mode
Reach level 15 in Spin mode
Reach level 20 in Spin mode
Send three balls outside the green circle in a single shot in Magnet mode
Win a Level 15+ Arcade game with 90% or higher accuracy
Complete 10 Magnet levels with the cue ball never leaving the green circle
Achieve a multishot of 3 balls in Arcade mode
Have 4 balls in the red ring at the same time in Spin mode