Concentrate on grabbing red rings in one playthrough and try not to get hit sometimes a S will follow. Grab a guide on YouTube to show you locations of rings, just pause game watch a little then copy.
Then tidy up levels that haven't got a S rank
I noticed finishing level with High amount of rings is important, and using wisps where can.
Rival rush just takes practice, take a look on some videos on YouTube, there's always a little trick that can boost you ahead normally a rocket wisp or a laser etc
The boss S ain't as hard again check out a video on the boss levels.