The Tour Challenges are the fastest way to get attribute points. Unfortunately, as you progress they become insanely difficult, even on Standard difficulty. However, there's no penalty for putting it on All-Play temporarily to beat the challenges. As you beat them, you will eventually hit Milestone levels that will give you TONS of attribute points.
You get attribute points just by doing things while playing normal rounds in career mode, but only very little at a time and as your golfer progresses you'll need more and more of them to upgrade each category.