Here is the full list of all 16 Legends of Snooker: One Shot achievements.
Complete the tutorial
Finish 5 levels
Finish level without miss
Finish 10 levels
Finish 30 levels
Finish 60 levels
Finish 80 levels
Finish 100 levels
Hit the black ball 120 times
Hit the another ball 20 times
Don't hit any ball 10 times
Hit the white ball 10 times
End the game
Finish level without miss 30 times
Set twice in succession without missing
Hit another ball in the same move you hit the black ball.