NiGHTS into Dreams...

This is actually much easier than it sounds, it's all really just a matter of knowing what to do. So here are some pointers:

First order of business: The Ideya capsules. Break them. Get your 20 orbs and break them as fast as humanly possible. You get a score bonus based on how quickly you destroy the thing. In addition to that, destroying the capsule will make anything you pick up before reaching the next checkpoint worth double points.

Once the capsule is down, you're free to go at your own pace. No need to go for the checkpoint right away, there's no time bonus for that unlike the capsule. Pick up everything you can find (especially the orbs, as reaching the checkpoint does give you a bonus for those). Do multiple laps by flying over the checkpoint. You won't move on to the next course until you actually fly through the checkpoint. Feel free to head to the checkpoint once you think you don't have enough time for another lap.
(I strongly recommend ignoring this advice for Stick Canyon Course 4, unless you are very good you will probably only have time for one lap)

If you get into acrobat time, just run into the ceiling and start mashing those trick buttons. You'll rack up a big trick combo fast, and huge points along with it.

As a general rule of thumb, to get an overall A rank, you need to get an A rank in at least 2 courses, and at least a B rank on the remaining ones (though if you cut it close, you can get away with lower. I got an A, two Bs, and a C once, and I still got an A overall)

Bosses are pretty self-explanatory. Time to go fast again. Killing bosses quick and without taking much damage will multiply your entire score, up to x2 depending on your performance. This could very well be the deciding factor in whether or not you get an A. Thankfully the bosses are not very complicated, so memorizing how they work should be no big deal. Remember that once you've cleared a stage, you can freely practice the boss without having to play through the entire stage again.

Twin Seeds work slightly differently. The capsules double as the checkpoints in this stage, so going fast is really all that matters here, but it's still a good idea to try and grab anything in your path, as the checkpoint will give you both a time bonus and an orb bonus.

Note that you have to get an A on Twin Seeds with both characters in order for the achievement to unlock. You do not need to get an A on Spring Valley Christmas.