These pointers should be taken with a grain of salt. I've only logged about 25 hours in this game so far but I'm starting to get it down despite the fact that it's a BIG game.
As in real golf, winning the better equipment (and skills) helps but the main place you're going to improve your game is your own skill both with the controller and making good decisions.
One of the things I've discovered is that I'm really good with clubs using less than 50% power or 100% power. The reason behind this is once you start going over 50% power, the power meter starts declining after peaking and your controller starts to vibrate. This makes selecting the proper amount of power difficult. Under 50%, you can pretty much just move the power meter where you want. Getting 100% power is also pretty easy to do consistently with practice. All this means is that club selection becomes pretty easy once your distance is determined. Allow for some yardage for rolling sometimes (using wicked backspin on chips is a must and topspin on drives adds some extra yardage) and pick the club that fits the distance.
Your right thumb makes an arc when using the thumbpad normally. This makes it difficult to consistently avoid slices and hooks. I've found that putting my thumb BEHIND the controller and pushing the thumbstick straight forward really helps with consistency. Holding the controller down by my waist as opposed to up by my chest also seems to help.
The only course where I've found that clubs/ball make a substantial difference is the Crusty Leaf. The trees make such a low canopy that you really want to reduce your loft as much as possible.
The easiest of the skill improvement challenges for me was the chipping set. I've completed all of them and only the last one required any equipment/skills beyond what you start with (you need wicked backspin and some pretty good distance along with really good accuracy). To win the chipping ones, select a target that will give you the points you need that fits the balance between more points (fewer accurate shots per round needed) and ease. Practice with this target until you're good. Restart the session. Win your skill points. The course and targets barely change from reset to reset and seem to only cycle through a small handful of differences.
The driving set was the next easiest for me. Once you're able to smash the ball at 100% about 95% of the time, these are cake. Just make sure your skills/equipment give you a shot that's at least the average you need and hit 10 perfect shots in a row. On the last challenge, you'll need to make it through the hole in the back fence. In addition to GREAT distance skill, you'll also need a great driver, ball, and lots of topspin.
The putting challenges are my bain. I'm a really inconsistent putter. The only advice I can give here is practice. It'll help both your game and the challenges more than anything else. Also, be sure and turn on the topographic grid with the white button. It really helps. Something else I found that helps a lot is selecting holes where you don't have to go across any inclines or declines to make the put. I was able to finish the first two putting challenges that way.
In terms of skills, I'd improve them in the following order.
I'd do accuracy first because it really helps cuts down your score when you need to avoid sandtraps, water, trees, etc. If you've played skins against Doc Diggler, you'll understand why it's better to be accurate than to be able to smash the ball into neverland.
Control is also important because you'll need both the backspin and topspin for the chipping and driving challenges and for your game.
Distance is nice and an eqo booster off the tee but that's about it. It'll rarely take a shot off your score. Hitting the ball an extra 20-30 yards will usually just allow you to use a smaller club on the next shot instead of reducing your score on the hole. Try a skins game against Doc Diggler and you'll understand. I can outdrive him by about 30 yards yet we split holes about 5-4 (him ahead and 50% ties). This means that in 18 holes we have 9 tied, him with 5 and me with 4 despite the fact that I can drive 30 yards further off the tee.
Finally, composure. Once you've gotten decent at the game, you'll spend most of your time either "Smokin" or "In the Zone". I usually only have to beat my caddy about once a game. This means improving your composure isn't that big of a deal since it's usually doing really well anyway.