Ok, I watched the INTRO TUTORIAL and it basically explained everything (which is pretty much what you said danmaku, but I'll try to lay out everything just to be more clear):
When in ship mode:
normal shot = gets blue gems and builds the circle around your ship, each symbol on the circle will become an aggressive shield when in ninja mode
hold shot = gets green gems and builds your ninja mode green meter
The more of each meter you have already, the faster the meters build.
When in ninja mode:
normal shot = gets blue gems, you never actually use this imo
hold shot = WHEN FIRST PRESSED WILL FIRE OFF ALL YOUR BLUE GEMS TURNED SHIELD which will fly forward and cancel any bullets and each one that hits an enemy becomes a SWORD (up to 16 max swords). Afterwords your hold beam will get mini-swords that build into regular swords and also create SPAWN BULLETS everytime you kill an enemy with hold shot.
When changing back to ship with SWORDS:
-They fly forward and create giant points, these giant points SHRINK quickly over time so you want to rush forward and collect them as they spawn.
Also, I think you need at least half of your blue gem meter filled (it will flash at 50%) to fire enough blue shields to get max katanas if they all hit.
So basically, not having watched any replays or read any guides it seems to me after playing for a few hours this morning that the key to scoring is:
(assuming you have some green meter at the very start)
1. Stay as a plane and use normal shot to build up your blue gem meter to 50% (it will flash gold)
2. Once it's at 50% and there are enough enemies in your path that all your shield bullet cancels will hit something, switch to Ninja mode and hold shot to launch your shields.
3. Once they've fired off, hit enemies, and returned as giant swords, wait until there are lots of enemies in your path and then switch back to plane mode and fire off all your swords.
4. Chase down your swords and collect all the giant score icons while trying not to die
5. Build up some green meter again. YOU DON'T NEED TO FILL IT. You only need enough time in Ninja mode to switch in, fire your shields, wait for a good moment and then switch back to plane mode. Usually if you have like 30-40% full green meter it'll be enough.
6. Repeat step 1
The variances are that you tend to want to use normal shot on grunts to build blue and hold shot on bigger enemies to build green.
BOSSES: The way to maximize your score is to make sure you kill them with a giant sword launch for giant score points. THE PROBLEM with this is that bosses don't give many blue gems. This means if you do the ninja switch bullet cancel -> plane switch giant sword cancel in the first 1/3rd or second 1/3rd of the fight to save your ass and do massive damage (because 16 swords grinding the boss is how you really do good damage against them), you're not going to be able to build up enough blue gem to do it again at the end to deliver the final hits and get the giant score points. So really, if you want to max your score, you need to save your ninja mode switch and plane switch back until the very end of the fight where the boss has like 10-20% HP left. The trick to surviving to that point without any bullet cancels of ninja mode slow motion is BOMBS. AFAIK there's no penalty in score or either meter for bombing, so USE YOUR BOMBS to save your ass and let you hold onto your blue gem meter until the boss is almost dead. The problem is that if you get hit once and die your blue gem meter resets and you've lost your chance.
That being said, sometimes it's best to focus on surviving over points and bosses are one spot where that rings true because if you beat the boss and get the stage end bonus, the amount of points you're going to get there and at the start of the next stage are MUCH greater than any amount of points you would have gotten from killing the boss with giant score points. When I was doing runs trying to save my swords to kill the bosses I'd often die and only make it 1-2 stages in. When I focused on survival at times I needed it, I got to stage 3-4 and had a much higher score even without the boss finishing bonuses.
Also the game auto-bombs if you have 3-4 bombs and when it does it USES ALL YOUR BOMBS UP. So don't let it auto-bomb, if you're in a pinch HIT BOMB. Bombing helps a lot here for keeping your score up.
Anyhow, using that strategy I had a 108 million point run this morning. Nothing amazing, only ranked ~250 on the leaderboards, but I'm a casual (aka, not that great) Cave/shmup fan and it's not often I make it in the top500 let alone top1000; so I'm pretty happy with that
Game is a lot of fun. The constant switching back and forth intense high scoring gameplay reminds me a lot of Futari, which I also really loved. I like high risk, high reward scoring systems in my shmups since I never go for 1CC because I don't have the skills so I just try to maximize my scoring in the early stages.