Kotohime is all about planning and foresight. More than most characters, she rewards you for "screen watching" and understanding some of the game's more subtle aspects. She gives you a lot of control over the flow of the game, but you have to use that control wisely to get the most out of her.
Let's start with what I think is her most defining trait: the significant delay on her spell attacks. This delay means her spells need to be timed differently from any other character's, and the number of factors you can realistically take into consideration when choosing your timing is more limited. For example, let's say you're playing Mima. What do you think about when you cast Mima's spell? Some important things would be: the formations which are currently on your and your opponent's screens, the formations which will appear after these (assuming you have this knowledge), how soon and how completely your spell will be reflected based on your opponents formation, how well your charge attack can clear or avoid clearing the formation you've currently got, your current position and potential mobility in the immediate future, which fireball phase you're in and how long before it shifts, and whatever dodging needs to be done in the meantime for the sake of your survival. Nevermind that truly keeping track of all this requires having a swirling galaxy for a brain, my point is that it's a lot. But now let's look at Kotohime. The first thing to realize is that, for Kotohime, most of the more "immediate" factors (current formations, current position, the impact of her charge attack) are actually pretty unimportant. If you can anticipate the next formation or two, this can be very useful, but in practice it's rarely possible. So what does Kotohime have to think about? There are basically two critical things, and one of them is uncommon: whether or not you've recently triggered a level 3 spell, and which fireball phase you're in, or more specifically, which phase you will be in in about 5 seconds. If you trigger a level 3 but then cast a level 2 before it explodes, the level 3 is often retroactively transformed into a level 2, and if you're not prepared for this you may get a surprise shitstorm to the face. But in general, the most important element to consider when choosing your spell timing is the fireball phase. Kotohime's spell takes about 5 seconds to explode, and the phases last 5 seconds, so if you want the spell to explode in focus phase you should cast it right at the start of the preceding scatter phase, or in other words, every 10th second.
Now, the timing for the initial casting may be easy to choose, but what you do in the next 5 seconds is very important. Basically, all of the factors which you would normally think about when casting a spell (but couldn't because they were too far into the future) will quickly reveal themselves to you in the time before the bomb explodes. The key now is to guide things in a favorable direction. Let's look at the general idea step by step. First, the formation you've got on screen at the moment you cast the spell is not going to be the one you use to reflect the shitstorm. The formation that does the reflecting will be either the next one, or more commonly, the one after the next one. The general idea is to remove the current formation, then remove the second just before the bomb explodes, and then use the third formation to reflect. If the first formation is one of the few that can be stalled an extremely long time, then you may stall that one until just before the bomb explodes and then reflect with the second formation. When the shitstorm arrives, it's important to be ready to macrododge the pellets even if you've got an exploding formation to shelter you, especially if the game is in focus phase. In doing this, it's important to understand that when fireballs are created, their aim is already set in stone, but pellets do not choose their aim until they materialize at the top of your screen. For example, let's assume you're right in the middle of the screen with a small formation exploding directly above you. At this moment, your spell explodes on the opponent's screen and is totally reflected. The instant this happens, you should dive to the left wall, so that even as all the pellets and fireballs come flying to the top of your screen, you're already on your way over to the left. The fireballs will still be aimed to the middle, since that's where you were when they were created, but the pellets will aim at the left wall. Now you macrododge down and under, returning safely to the middle. (Kotohime is fast enough to consistently macrododge the reflected spell regardless of whether you reflect any of it as long as you're prepared and nothing gets in your way.) It's also very important to keep an eye on the opponent's screen before the bomb explodes. Because you can see the bomb's exact position, approximately when it will explode, which formation the opponent has on screen, and where they are shooting it, you can predict almost exactly when and how your spell will be reflected. You can see, for instance, if the spell won't be reflected all at once, but rather will be reflected late after the bullets have spread out, and react accordingly. It also helps to understand that the further the point of reflection is from the inner wall, the longer the reflected bullets and fireballs will take to reach your screen, and similarly, the further you are from the inner wall, the longer aimed fireballs will take to reach you.
Another quirk about Kotohime is that her boss attack barely uses any pellets. This makes it very safe. In fact, from a scoring perspective, it's existence is actually counterproductive, since it tends to distract the AI from shooting the formations. Nonetheless, between the safe boss, and the careful precision with which shitstorms can be created and reflected, Kotohime is a character who, when played thoughtfully, can score very high very safely. If you're swimming in energy and want to take greater risks, start casting spells every 5 seconds rather than every 10 seconds. If you want the game to cool off, just stop casting spells. Your boss attack rarely backfires and suppresses the AI very well.
Now let's look at some particulars.
At the start of each round, I think the usual goal should be to build up enough energy to cast a spell at 20 seconds. You could cast one at 10 seconds but it's almost never possible to get enough energy in time. Triggering a boss attack before you've cast your first spell seems to be a bad thing more often than not, so don't go out of your way to preserve your spell points in the beginning. If you lose a round and start the next with enough energy for a spell, you have two options. Unlike most characters, who can cast a spell after about 3 or 4 seconds and get it reflected by the first formation right at the start of focus phase, Kotohime can't quite get her spell out fast enough. If you cast the spell as soon as possible, it explodes towards the end of focus phase, but the first formation tends to show up a little too soon. The most effective response to this seems to be immediately killing the first formation with a charge attack and then reflecting with the second, but this is a little unreliable. The safer option is to just wait and cast the spell at 10 seconds. If you've only got the energy for a single spell, that's the one I would pick. If you've got a lot of energy though, may as well take the risk and cast instantly.
Kotohime's charge attack is great for some things and terrible for others. Bosses melt when pointblanked by it, and it invariably destroys any fireballs that cross it, making it reliable for self defense. It's slow speed makes it hard to use for chaining though, and playing Kotohime against characters whose extra attacks block bullets can be a struggle. It's also difficult to reactively clear a formation just as it passes over a boss that's about to shoot a bunch of pellets. This is especially annoying against bosses who move while shooting, such as Rikako and Ellen. I think Kotohime's most favorable opponents (for scoring) are Marisa and Mima.
As mentioned before, you can actually convert level 3's from boss panics into level 2's. This can be very lucrative, but keep an eye on the opponent's screen to see when the bomb will explode.
Boss cancelling is very good for Kotohime since you'd usually rather not have her boss on screen anyway.
It can be very tempting to try to speedkill Yumemi's boss attack, since you can indeed sometimes kill her before she attacks, but this is a bit of an illusory advantage. You generally can only kill her that fast when she was going to do one of her weaker attacks anyway. You need near perfect timing to kill her before she does the cloud (and if you over commit you just take it to the face), and even preventing the swirl is difficult. Further, if you try to speedkill before the swirl but aren't fast enough, you now probably don't have time to use another charge attack to go through the swirl with i-frames. Speedkilling her has its merits of course, just be careful.
And here are a few gameplay examples.
https://youtu.be/nZO6AdrkLKc?t=1553
In this case the first formation takes a long time to clear, so I reflect the fireballs with the second. I destroy it on the right to make the fireballs appear sooner.
https://youtu.be/nZO6AdrkLKc?t=895
A level 3 converted to level 2.
https://youtu.be/nZO6AdrkLKc?t=2136
A surprisingly viable way to dodge shitstorms when you're too low to properly macrododge them. Dive upward into the space created by exploding fireballs, then cut right.
https://youtu.be/nZO6AdrkLKc?t=2327
Another example of how being near the inner wall makes the fireballs arrive sooner. If I had tried the exact same thing on the left it would have failed. Also shows how starting with an instant spell tends to cut it very close. Alternatively I could have speedkilled that formation and then reflected with the next.
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