While it would be hard to provide a true "solution" to all 75 challenges, I thought I could provide some general challenge tips that would be useful.
1.) PICK YOUR POWER: choose a master appropriate for the challenge at hand. Splork is well-suited to full clear with tightly clustered pegs. Hu is good for the marathons and large orange peg counts. Warren is essential for some of the score challenges. Even Björn can be helpful in making sure it's you who gets the fever score in master duels.
2.) USE THE RESTART: the pause menu lets you start the challenge over easily. Don't be afraid to reset the board if you don't get good green placement (ex: Splork gets a green that's not near many other pegs) or if you don't like your first shot. For some challenges I even resorted to restarting if my first shot didn't earn me an extra ball or Warren didn't get a triple score.
3.) LONG SHOTS and FEVER METER: two easy ways to run the score up. You may not be able to see the whole path a shot will take, but with a bit of practice you can nail a long shot every time for 25k (or 50k for super long). Also, focus on the orange pegs early but then leave a couple. Once you're down to 3 oranges all you have to do for 25k and an extra ball is hit the purple and four blues.
4.) ULTRA FEVER SCORE: a somewhat less easy way to run the score up. But for some of the higher single-level score challenges remember that if you can clear all the pegs the bonus ball will always be 100k. It is, after all, pretty disheartening to come within 25k of the required score only to watch your bonus ball take an intricate but seemingly inevitable series of bounces toward the 10k bucket.
5.) SPREAD THE LOVE: don't allow yourself to get frustrated on any one challenge. Not feeling the high scores? Go for a marathon or master duel for a bit and come back. There's no bonus for doing them in order.
6.) MIX IN SOME MULTIPLAYER: you can learn a lot about the game's nuances from watching other players. Take a break once in a while from challenges and go for the online achievements. Obviously, the better you are at the game, the easier the challenges will seem. And I think the fastest way to improve is by watching and learning as pros whip you in multiplayer.
Hope this helps!