The various challenges will be varieties of the following:

Jump Shot - Pot a ball whilst using a jump shot. Note that it will ONLY count as a Jump shot if the cue ball actually jumps a ball. This will not count if you just make the cue ball jump on the table, but not over a ball.

Bank Shot - Pot a ball which target ball hits a cushion (NOT pocket edges) and bounces into a pocket.

Kick Shot - Pot a ball where the cue ball has first come off of a cushion (NOT pocket edges) before hitting the target ball, which has then been potted.

Combo Shot - Pot a ball using a 'plant'. E.g. Cue Ball hits the 1-ball, which is the target ball, and the 1-ball bounces into the 2-ball, and the 2-ball gets potted.

Swerve Shot - Pot a ball by swerving the cue ball around another ball to get to the target ball. This will not count if you just make the cue ball swerve on the table, but not around a ball that is in the way of the target ball.

Score - Have a total score of the given amount by the end of the match. This is where you CAN use jump shots, swerve shots, kick shots, bank shots, and all other manners of tricks to boost your score, even if you don't need to jump a ball, swerve a ball, or bounce off of a cushion.

Shot Score - Get the given amount of points in a single shot. The highest requirement I've seen for a shot score is 10,000 points. The best way I found to do this was to use a jump & swerving shot to bounce off of either end cushion to perform a Combo Shot. This gets around 13,000 points if it's a good shot.

Pot Streak - Highest I've seen for this is 7. All you have to do is pot the given number of balls without missing a shot or fouling.

Note that challenges will NOT be completed if you do not win the game/match. You must win the game/match that you complete the challenge in.

Hope this helps.