The suggestions here to do the challenges are the way to go. When doing the challenges, enable manual ball spin and disable wind gust. Use all the shot meters, distance information, and aiming tools available. You don't get a bigger reward for completing challenges based on higher game difficulty, so use that to your advantage.
Also, put a lot of points into your around the green skills. A lot of the challenges (way too many) require you to hole a shot from off the green, and having high around the green skills helps considerably with those challenges.
Be aware that some of the challenges that require you to play 9 or 18 holes and post under a certain score won't give you stars when you complete them. To avoid wasting your time, maybe do some research on those ones to see which ones are still broken.