So
here's that replay. I do some retarded scoring things in here so I'll add a couple notes here:
1) I shot at the big guys in the beginning unfocused because it gives time orbs, but you should switch to focus to kill them faster so they fire less. That'll give you more room to POC the power items they drop.
2) There are a few points where I don't kill some of the 'chain-throwing' familiar dudes so that I can kill them when they spawn the second 'spread' of familiars. Obviously that's unnecessary for survival, so just kill them all ASAP. You handled them really well in your replays, so don't change your strategy here.
3) I bomb a few times in the second half of the stage so I can collect point items. You handled those portions of the stage just fine, so one bomb should be all you need (for the part with the purple bullets followed by the aimed blue bullets.)
3) Don't spin around Mokou for her first nonspell haha
4) I move more than necessary on Xu-Fu's Dimension because I want to graze a bit more, but don't actually do that. The idea is about the same, though. Sit at the bottom of the screen and you only have to worry about the cards that are on the very bottom line. Just start on the far left side, then slowly tap over to avoid the diamond bullets she shoots and the cards at the bottom. This card is an easy capture like that.
5) Shooting unfocused during Possessed by Phoenix is just to get time orbs. Don't actually do that. Otherwise, the general movement pattern I used should work fine.
6) If you know how to capture Imperishable Shooting please tell me :<<<<
Basically, for the stage portion, you should be killing dudes faster. The big guys that summon familiars to circle themselves can be blown away before they shoot anything that would require precision dodging. You handled Flying Phoenix better in your second replay, but if you copy the method I used you should be able to capture it pretty easily. Same thing for Honest Man's Death.
In terms of the later spells, Phoenix's Tail is just straightforward dodging. It helps if you try to read ahead into the mess a bit. For 'Woo', it's not too bad if you can misdirect the last wave of the card. Fujiyama Volcano is a bitch and a half, but the method I use works for me pretty decently. It's hard to copy, though; you have to stay under Mokou as long as possible so you kill her before it gets really shitty to dodge. It seemed like you went into it blind. Most of the shots are pseudo-aimed at you, so you want to misdirect/stream the big explosives and then stream the fast red bullets. The other bullets exist purely to piss you off, unfortunately. It's really hard.
For PbP, I just fly in a circle around the edge of the screen for the first wave, then slowly tap up with the beat for the second wave, and then fly around in a circle for the last wave. The explosions are pretty tiny, so don't worry about moving too far there. Hourai Doll is basically 'fly around in a circle in the center of the screen' with extra bullets thrown in after a while. It's way easier than stuff like BoLaD and Q.E.D., although it's tough to capture unless you're good at really tight dodging.
You're pretty good, so I think you can clear the stage if you just go into the bossfight with more resources and master her early cards. The biggest wall for me was Fujiyama Volcano. Unfortunately there's no real good way to learn that spell outside of playing it in spell practice a whole lot and hoping you don't fuck up, because if you have to bomb the timing and patterns get all messed up and you're pretty screwed :X Keep at it! You can do it!!