I'm sure you're not alone as to me the 3D stages also used to be very challenging for a long while, especially later on in the game!
Rings that are above water but in the middle of the screen are fairly enough to get, even if you just start spamming jumping out of water, there is still a good chance you would get them.
Those that are close to the top of the screen though you have to use the B button right before you hop out of the water to jump extra high and you'd only get one shot at it. This, of course, will only get harder the further you go on since there is going to be more enemies in the water that you'd also have to pay attention to! Which is also why you would want to save that Hunter Song for later =)
So my advice is to practice a lot, it helps the first level is right after the Home Bay, so there's no problem starting it over. It's crucial to get the timing just right on those aerial rings and after that you should be able to predictably get them.