First tip: use an easier team, Sakuya is an awful character and that team is only really good for scoring (because of Remi's graze range, though solo Youmu is still better there afaik). Border team is probably the easiest for beginners, though Netherworld team is pretty amazing too if you can handle unfocused Youmu well. Magic team is kinda meh, solo Marisa would probably be better than them.
Stage 1 - Letting items drop offscreen and letting fairies fly away is something you should try to avoid. PoC before the items drop, kill everything as quickly as possible if you can manage it. Scarlet team specifics, you should try to move under enemies (like that big fairy) before you switch to focus. Sakuya's shot should only be used for popcorn enemies, familiar killing, and for repositioning yourself. Try to keep both of Remi's shots under the boss at all times (if possible)
Stage 2 - Get more comfortable with the top of the screen, and PoC more. I have a feeling this statement will hold true for your whole run. Be aggressive, it pays off! Just don't be suicidal =p. For cards like Mystia's where the familiars will just leave the screen, it's often better to just ignore them, since it won't make decrease the bullets that much. At least for this team anyway, Youmu and Marisa are significantly stronger than their partners, so non-focus is always quite effective for them on bosses - the point is to focus more on the boss in any case.
Stage 3 - Killing Keine's familiars is generally a good idea, so you're doing okay there. I can't think of much else to say here. Maybe stay off to the side a bit on Keine's nonspells when she respawns her familiars so you don't get trapped. Or at least on the first, the second one might be worth being under her for to kill them off a bit quicker before they start to shoot too much.
Stage 4 - I noticed it a bit before now, but here's where it starts to matter more. Focus-kill anemies with lots of familiars, since when the fairies controlling them die, the familiars will cancel the bullets around them. They'll also generally die faster, since the familiars won't be acting as meat-shields. You'll have fewer bullets to deal with, and it'll help your score as a nice side-effect. For Reimu... Well, you've got that right! Stay focused for anything involving yin-yang orbs, unless it's just a quick tap to reposition Remi's familiar. Practice Concentrate a bit more until you can to it fairly consistently. The trick is to aim the amulets to the extreme side and a bit up the screen when they turn purple. Unfocus to get over there more quickly. For the last card, if it helps you at all, you don't really need to move horizontally much. You can just wait for the red/white to crossover, move up, wait for the ones under to crossover, move down, repeat. Just align yourself to the point that it'll happen at and don't forget about the white bullets.
Stage 5 - Practice the hell out of this one. As a stage, it's really easy, but if you don't know all the enemy spawns it'll be quite good at clusterfucking you. Particularly those little fairies that come in groups. Basically you just want to kill stuff before it can overwhelm you. Second Reisen spell, practice that a bit. Try to figure out where the empty spaces will be the largest when she unfreezes. Practice the third one too, since I've noticed that you're not very comfortable when there's a lot of bullets closeby. Remember, concentrate on the openings, not the bullets themselves! For the last spell, it doesn't need much practice since it's probably easier than Mystia's cards, but I will say get off the bottom. Since it's a hard spell to explain with words, I'll just use
this pic so you can where the space I'm talking about is.
Stage 6 - Eww, 6A's got nasty bullets on the pre-Eirin fairies... Try to kill them before they can shoot more than a few bullets. Try to start Eirin's midboss from the extreme left (or right) so you don't get walled. Eirin's second spell, hug the bottom and only move horizontally. 99% of the time, the blue bullets won't spawn in a way that can kill you if you don't move vertically. Also, use a continue and finish the stage to unlock 6B. Kaguya is so much nicer.
Hopefully I got everything. I was going off your replay specifically, so Remi/Sakuya-specific stuff may not apply if you decide to drop the Scarlet team. To quickly generalize the others, the border team will mostly use Reimu for stages (Yukari for stronger enemies) and Yukari for bosses (Reimu on occasion for familiar-popping/quick movements). Netherworld focuses on using Youmu for damage and Yuyuko for fairy-popping and tight dodges. It really helps to be comfortable with no-focus movement on high-speed characters for them. Magic team focuses on not focusing. No really, Alice will just bring you down, so don't focus for anything other than maybe a couple familiar-heavy fairies or really tight dodges.
And I know I've said it a couple times already, but I can't stress it enough: expand your comfort zone. Do some throwaway runs, do some stage/spell practice on higher difficulties, whatever you need to do to help yourself adjust to moving around bullets quickly, accurately, and reflexively (maybe that falls under quickly...). It's probably the second-most valuable skill you can have (after dodging =p). It helps your score, it helps your survival, it helps your damage output... It helps everything!
