The ultimate strategy, as I discovered through much trial and error:
Because no matter what you do, you can't really choose when the opponent dies, you instead have to outlast them. Meaning, you want to drag out the fight as much as possible.
In short, you want to get to max charge ASAP, especially before your opponent can reach it. However, if you just blindly fire for points, you're going to cause a bunch of boss attacks to be thrown around, and more often than not (because the computer is a cheating bastard and knows where the spirits are going to fall), you're going to end up on the receiving end. Of course, because you obviously want the second extend, doing this may be worth your while at least once.
Anyway, the big strategy as I know it is to only blow up enemies that don't hug the top. No matter what, you want to avoid firing a boss attack through points because the computer will counter it. By destroying enemies closer to the bottom, you decrease the chance you'll blow up a spirit (which are worth HUGE points this way), and still fill up your gauge at a decent pace. Once you reach full power, wait until the opponent fires her boss attack. Once you see her starting to charge her gauge, start charging yours. As soon as she fires, fire your own to cancel her boss attack out and send her back to minimum power. Repeat this for as long as possible. When things get hairy, use your bombs.
Now, once you run out of bombs, you want the same general strategy. Instead of firing a boss attack though, you instead want to go hyper (by pressing the bomb button with no bombs and a full gauge). As Baity pointed out, there is a scenario where the AI is guaranteed to get hit, and while you're invincible, you can blow up as many spirits as you want to increase the chances of this, so just for here, go nuts. Just make sure you don't let the opponent activate a boss attack that goes on once it wears off.
And that...is my strategy. As for recommended characters, I found I had the best success with Reimu and Yumemi (and I beat lunatic with Yumemi, because apparently her crosses do well against the AI, though not Aya level or even Shikieiki level).