I don't know shit about playing Yukari, except that I hate her.
Yukari is a zoning character whose main strengths are neutralizing enemy danmaku and controlling the ground. She has a relatively weak aerial game, so the usual "jump up and control from the air" that works for much of the cast is much weaker with Yukari. Denying the opponent the aerial approach will allow Yukari to control the game, so she must play defensively until she gets a decisive advantage. Yukari is very matchup-specific, meaning that she is reactionary and can't stick to one gameplan for every matchup, unlike Yuyuko or most rushdown characters.
Yukari's offensive momentum is fairly strong. She can turn a blocked normal into a cornered opponent fairly easily, much like a typical rushdown character. However, she cannot generate these situations as easily as most rushdown characters; she must play defensively and punish enemy mistakes in order to get these advantage situations. She lacks airtight strings, but she has many options to punish grazing, which can lead to fairly high damage. A good arsenal of 1-cards also helps keep blocked 623Cs from being punished. In general, if you're looking to graze punish, make sure you have a spellcard ready.
The main tool in Yukari's arsenal -- the one that she wants to use ALL the time, is her B bullets. If Yukari's opponent isn't specifically looking to punish her (or can't), AND her opponent doesn't rape her bullets (eg. Utsuho), Yukari should be trying to get B bullets on the screen constantly. Her response should depend on the opponent.
*If the opponent tries to graze them and you are in range: DP; if you're in the air, rush down
*If the opponent tries to throw danmaku through it and you're in range: DP
*If the opponent tries to graze safely: get into a safer position and throw more bullets, probably B
*If the opponent tries to graze to a position to throw danmaku: throw C bullets that will hit them, if none, graze safely and try to throw more B bullets
*If they block: RUSH THAT SHIT DOWN
As you can see in the above flowchart, the B bullets into DP is a very important mixup for Yukari so keep it on the back foot at all times. You can also substitute teleports instead of a DP to hit an airborne grazing enemy, but beware as they basically throw momentum away if you whiff.
In some matchups, the opponent will have rape danmaku that will horribly punish you if you try to throw B bullets. You still need to throw them but be very careful, especially against lasers, Patchouli, or Oni Spirit Bomb. Don't throw bullets predictably, and be content to jump up and down doing nothing. I am not sure what to do in the Utsuho matchup.
If you are on the ground, you are fishing for the enemy to get in range of your ground melee. 6a will mess some bitches up if you use it as antiair from the proper angle. Walk backwards in order to get this angle and be evasive if the opponent won't give it to you (or just jump back and do nothing or throw B bullets). If your opponent is consistently getting into your close air zone above your 6a range, you can throw anticipatory 2b to beat melee. Be careful to backdash or highjump cancel early because air-to-ground danmaku could happen. Make sure you throw it early if you throw it at all.
Actually, this brings up a very important point; Yukari must make anticipatory decisions to close down the opponent's aerial approach. 2b is very important for this, since it makes close air melee impossible for the enemy. Remember how I like to shoot bullets at Iku when she's looking to close in for j2a? That's kind of what 2b does, but you have to throw it early or it's crap. Again, as soon as you see the enemy jump you need to be decisive and either jump back nothing, jump back bullets, 2b, or 6a antiair if they're in range.
66a can also be used as an antiair against many characters (non-Iku, non-Yuyuko j2a) going for a predictable close air attack. Be careful on spacing it, but because it lowers your defensive hitbox a LOT it works pretty well. Use sparingly, air-to-ground bullets suck and rape your face. Again, be decisive. If they jump, you need to choose what to do and commit to it.
If both of you are on the ground, your default answer should be 66c; this is actually a bad idea but it is important for conditioning. If your opponent jumps, 66c will catch them, it will beat all melee dash forward type stuff and it grazes so it beats danmaku too. If your opponent blocks, he is at advantage but you can cancel into a special (don't do a DP). Do this every time your opponent lands on the ground in a neutral or advantage position (her at advantage, not you) until she stops jumping or doing stuff. If you're too close, just do 3a and cancel it into bullets if it gets blocked. If you're both on the ground it should only whiff if she jumps back, which she can't do anything except setup danmaku (which you can punish with low j5c). Once your opponent stops jumping, you can do dash-in 2a spam and take the advantage for free. This probably will never happen except against me. Note that, at certain distances, the opponent can jump back bullets to punish you. It's mainly important for non-Yuyuko characters, as Yuyuko has no way to punish 66c other than getting setup danmaku for free (which is kinda bad for you). Don't 66c at other times, ESPECIALLY if you are at advantage. If your opponent is likely to just fucking block then just fucking rush down.
If your opponent likes danmaku, use 5c, 6c, or j2c to beat it depending on positioning. Predict the danmaku and beat it; don't stick out C bullets at any other time except in block pressure. I can't stress this enough. If the enemy isn't throwing bullets or attacking, don't throw C bullets. It's a fucking mantra: don't throw C bullets unless they're going to get blocked or you are predicting enemy danmaku.
If you're in the air and she's on the ground, just throw B bullets and try to get back on the ground. Remember that if you throw B bullets and she stays on the ground, you will be at advantage so rush down, don't do 66c or some garbage.
Don't DP to beat danmaku unless you can't do 66c or you need the startup graze; your DP comes out slower, travels slower, and is horribly unsafe. Obviously if you throw bullets and they attack somehow inside the range of your DP, your only option is DP or highjump cancel so DP is the clear winner there.
Yukari's offense kinda sucks by rushdown standards, but she has some shenanigans. The main biggie is that you can 2a*n > 6a > 2c into a "mixup." Mix up the number of 2a you spam to avoid being unpredictable. If your opponent is a shitbag who does not know how to block low, 3a instead, otherwise 6a to overhead when she starts blocking 2a low.
In Yukari's case, her mixup is either DP or HJC9 j2c airdash j5a land repeat. 2c cancelled into DP comes out disgustingly fast and will beat any sort of jump bullshit. It will also beat anything except a reversal but a reversal at that point would be stupid anyway. If the DP gets blocked, supercancel or you will die. If you don't have a super, DP sparingly. Against fucks like me who jump out all the time in any gap, DP all the time. If I learn not to jump there, hey, I like free combos anyway.
Lemme repeat that again:
2a*n > 6a > 2c into...
--DP (supercancel if blocked and continue pressure)
--HJC9 j2c d6 j5a land repeat
--HJC9 j2a 236b (Bound to the Grave) loop (airtight in corner only)
The Bound to the Grave blockstun loop must be bordered if done properly. If you do the j2a too high, your opponent can just hit you out of it after it is blocked or counterhit your 236. You can also mix things up by doing 2a*n straight into 236b (because who would try to mash out of that?) and starting the loop that way.
Aerial pressure is a bit different. The main reason is that j5c/j2c bounce Yukari back a bit, making it hard to follow up, but j5b is slow as balls. The basic air pressure you should use is j5a j8a j5c D9 repeat. This is also your midscreen bnb air combo; Yukari has jack shit for air combos so your main damage will be from putting the opponent back on the ground. Yukari can do j5a j6a j5c loop until limit if she has her opponent cornered.
Yukari's main BnB varies somewhat. 5aaa 623c is the most reliable combo she has in many key matchups and it does shit balls for damage. It also DROPS WTF if too far away.
If you have Bound to the Grave, 5aaa 236b does more reasonable damage.
Among characters actually played by us, Yukari's real BnB combos drop on Reimu, Sakuya, Tenshi, Suwako, and Yuyuko. This means you probably don't need to learn them, but you should probably practice them once you've practiced the more fundamental stuff and need something to work on.
3a 2c 421c~6. Use it against everyone anytime you hit with 3a. Don't do the damn teleport if it's blocked and do a normal damn block mixup.
If 6a hits far from the corner, you won't land anything so throw some B bullets and get ready to punish a tech or play the wakeup game. If it hits close to the corner, you can 6a 6a 623c.
You know the corner combo but just suck balls. Learn to DP. This combo is easy and if you're having trouble with it, you're not practicing even half of enough.
--I think that this is personally Yukari's hardest matchup. It's not that bad, but probably her hardest.
--After blocking either 5aa (far swinging fan), 3a (low sweep kick) or 6a (overhead fan), you can DP and beat anything Yuyuko does. She can 2b and jump back and her B DP might win, so only use until she learns the counter. If Yuyuko has the true DP card, she can basically wreck you on block (DP fights lol). Sucks.
--Yuyuko can pretty much rule the midscreen though. If she just grazes and throws out safe C bullets and butterflies, you will eventually block something or get hit and lose. Additionally, Yuyuko does tons more damage than you.
--BEWARE OF 236 LASERS. B bullets are really unsafe in this matchup.
--For Yuyuko: Don't block anything, graze everything and use 5c and 6c whenever possible. Don't use normal melee pressure; mix it up (eg. 2a straight into 421 or 2c or something). Throw lasers liberally if Yukari's in range and doing nothing. Play like a bitch. Don't ever get grounded at the same time as her unless she is blocking or you are really, really far away.
--Yukari favored, but Patchy has answers to you midscreen.
--For Patchy: Don't get grounded at the same time as Yukari, and if you do delay your jump a moment to see if she does 66c. Yukari 5c will hit you if you 6c. Don't use bullets unless Yukari is not parallel on the screen with you (or in blockstrings/combos obviously)
--Yukari B bullets and Patchy 5c don't directly beat each other and are still threatening. Beware. Patchy 6c beats Yukari B bullets, so Patchy might fish. 5c beats her 6c if you cancel properly. BULLET RPS. Patchy metal wheel bullets are amazing in the matchup since they clear Yukari C bullets and cancel early.
--Patchy's close air approach is most dangerous due to her dense bullet air to ground options. You are better off jumping back if Patchy gets airborne without you punishing her with 66c.
--Patchy 4b HJC window is kinda early, so she can empty HJC to cause your DP to whiff. Don't DP randomly in normal blockstrings. The only gap is immediately after 4b (which is immediately after her melee). You can border anytime after blocking her ground melee; however, if she decides to hjc9 j6a you will get caught.
--Just stick to normal gameplan. NEVER get close to Patchy in the air, j6a wrecks all your options. Only do it if she's blocking or grazing your shit.
--This matchup is also hard. Technically Yukari favored, but I'm not feeling it. I think it's 5.5 Utsuho.
--All of Okuu's bullets are dangerous, and it pretty much shuts down your gameplan. You need an alternate one.
--Whore the ground like a boss. Okuu doesn't have good danmaku cover so 66c anytime she might be in range. Do the move like 300 times a round. Not even joking. If she ever jumps in, 6a or jump back.
-- Jumping back is really dangerous against Okuu unless she's also in the air. If you're directly above her, 2b is pretty good but make sure you're ahead of her 2c laser or you could get owned.
--Okuu 6b is so gay. You want to bait her into a situation where you can either 66c or DP her.
--If Okuu might not jump and wants to stay on the ground (that bitch!) use 66b. It's special cancellable too, so cancel that shit into Bound to the Grave and start the loop.
--Bound to the Grave might actually beat her bullets on the ground, iuno.
--If you actually get offensive momentum, don't give it up.
--This matchup is a free win for Yukari.
--Don't ever engage unless you're at advantage. I feel like a broken record here.
--If you're both on the ground... Suwako's dash actually gays your 66c here. If she is not yet dashing and you are at the right range, you can beat it. It's worth making some mistakes here to learn the proper range, but if she takes to the (under)ground, HJ back and throw B bullets.
--If you ever block a non-5a melee (including j5a), DP immediately after you leave blockstun.
--If you're both in the air, fish for C bullet positioning and fly away at all other times. If you can, throw C bullets, otherwise B.
--If she ever uses anything that is a bullet, 6c or jump back 6c depending on spacing.
--If you ever get advantage... you know
--This matchup is a joke. You can just runaway and deny Suwako everything.
--Different characters have specific tools but most characters can eat through some B bullets to hit you. Don't get hit, and don't block if you can avoid it. Graze defensively.
--If you're in the air and she's on the ground, throw B bullets.
--Throw C bullets if you're in line to do so and you're not both on the ground.
--Play defensively. You have the advantage midscreen so try your best to do nothing risky or aggressive until the momentum turns in your favor. If she grazes forward through your bullets and you're both in the air, you can punish so look for that. Otherwise, don't fucking dash into the opponent doing stupid shit.
--If you're both on the ground, 3a if you predict a dash in (and combo off it) or 66c if you think she'll jump, throw bullets, or do anything other than jump back. If you predict she'll jump back, YAY. Throw bullets.
--Follow the gameplan and don't rush. Just turtle and wait for opportunities. Don't engage unless you are at an advantage (she's blocking, airgrazing or getting hit).
--DON'T BLOCK HER BULLETS OR RISK DYING
--vs. Youmu specific: Cry a lot because her reflector is fucking gay and she can jump straight up bullets really safely