re: lunatic...
As far as I can tell from watching my replays and reading a bit, Shiki (and likely all characters, for that matter) dies at set times. Dies once at one minute and again at two. Not sure when she dies next as I've only beaten her on lunatic with hax characters (Aya, Medicine, Marisa), so I get a lucky death after that and it's game. Also, every time you lose, the timer from two minutes is reduced by about ten seconds; so after three losses she'll die a second time around 1:30. If that's a ratio, after three losses I'd think that I'd be able to watch her burn at 2:15 (assuming her third death is at three minutes), but it's either not a ratio or she dies a third time later than three minutes since I've made it past 2:15 with three losses and she's still lecturing.
I think offense is an illusion in PoFV when playing against the computer (outside of extra but then again they just run through bullets on extra). They're going to die when they die, and the only way they might not is if you aren't shooting anything. And even then they have a penchant for suicide. Edit: in this way I think the waiting strategy in the next paragraph will be effective on lunatic, but I haven't been on my game in a while so each time I've tried this I blew it too soon to yield meaningful results.
re: extra...
The easiest way to beat difficult characters on extra is to only shoot to keep the timer ticking down. If you don't shoot anything, the computer most often does not use any spells. So, if you only pick off the last fairy in a line (avoiding starting any chains, cancelling any bullets, or destroying any spirits) and repeat that each time the timer stops counting down again, you can get the timer down to zero or at least close to zero; at this point all you have to do is fire for a few seconds and the computer finds a convenient bullet. I'm not completely sure on this last point (a little rusty on pofv), but I think even if the computer leads off with a spell, if you don't fire and simply dodge it then it won't fire off another one. Again, usually.
My strategy against Shiki in particular is to go balls-out the first round to build up my spell meter to level 4, and after I lose I go with the waiting game. Still end up having a half minute or so of intense play, but it's much better than dealing with a full timer.
Of course, this waiting strategy should only be used when you have to since it's a score-killer and hence an extra-life killer.
misc...
fwiw: I've never had any luck with that stupid 'let the screen clear of bullets' strategy. If you're good enough to survive the walls that result (late in a match) from a lack of bullet-cancelling, you don't need to stop shooting to begin with. Dodge as much as you can and when things are intense keep building your spell meter and firing off level one spells; that way when things get too heavy you're already partway to a level two (fairy) spell.
Also, for Shiki: macrododge. You aren't going to make it through some of those barrages without immense luck, so use the entire screen. It is in this way that PoFV forced me to cheat on my micrododging lover and made me a better shmupper.
Also also, streaming is only useful with Aya. Just watch the walls. Edit: and I guess it works for a few other things like one of Youmu's dragon attacks, but it's still not a helpful tactic for most of the game.
Maybe none of that is new (I know I've read a couple of these points before but I'm not sure where), but I recall learning a good bit of it the hard way so hopefully this is not just a rehash of what everyone already knows.
