I wouldn't say that there's no trick to Yukari's Spirting Away. Personally I do the same pattern of movement every time, essentially: When at the bottom of the screen, and she tries to appear on top of me, I move diagonally upward (we'll say I went up/right, just for the example). When she fires danmaku, I move sideways (in this case left) to avoid the big bullets, ending up directly above Yukari. From there dodging the butterflies is easy, just let them go past. Then Yukari tries to appear on me again, and I move down, shooting her while backing up. When she fires again, I move right. The butterflies should be coming at me diagonally from here, and again, I just let them pass. She'll follow me again, and I just repeat the process, only this time it will be a "mirror" of the first pattern. Doing it like this lets you shoot Yukari without needing homing bullets. (Note that for some reason, this is much harder to execute against Ran's "Princess Tenko")
As for shot type, it's basically like Drake said. At the very least I'd switch to Reimu A. She also has homing, but some normal forward shots as well, which IIRC make her do more damge than Sakuya as long as you are under the boss. Not to mention Reimu has a smaller hitbox and more managable movement speed while focused. If you do best as Sakuya A then you must be doing something wierd.
And as for Double Death Butterfly, my best advice would be to not jam yourself against the back wall. You need to be able to see the upward bullets returning from off the screen. Even if you can't dodge this, it should only take one bomb to get through. (unless you're a wimpy character like Sakuya A)