I don't think I'd bother trying to get all of the rings in every special stage, although you nearly have to in the last one.
Seriously? That seventh emerald took me something like thirty tries. The goals are 150, 350, and 500. If you want to beat the stage, you can't pass the first goal with anything less than 165 rings, or the second one with anything less than 425. I think the final portion of the stage only has 80 rings in it total, so if you try to pass the second goal with the bare minimum of rings, you're [tornado fang]'d.
I did come up with a good strategy for it though! Specifically, the second section. It'll have you jump over a few sets of bombs to get the tag team tether. Once you've done that, pick up all the rings you can while dodging the bombs for a few turns, then you'll come up on a long strip of rings in the center of the half pipe with bombs on the outsides. Immediately after, a long strip of bombs in the center of the half pipe with rings on the outsides (with one row of bombs across the very end of the ring path, which you have to jump over). After that is another row of rings down the center of the pipe, with a single row of bombs blocking your path at the start of it. The game expects you to jump over the bombs, but run into them instead. It sounds crazy, but that row of rings has at least 6 10-ring bonuses in it, and if you jump over the bombs you go right past them. So if you hit that strip with say, 225 rings, you can come out of it with nearly 300.
After that, if you hug the left side of the half pipe to avoid the next few sets of bombs and pick up the tag team tether in the center of the pipe (right after you're forced to jump over a set of bombs from one edge to the other), you can speed up and loop around the pipe beyond that's lined with rings. The tether grabs enough of them to put you well over 400 if you manage to dodge the bombs at the end of the pipe (which is annoyingly difficult actually, but not impossible).