MOOGS'S GUIDE TO KILLING PATCHY!
TL;DR: Since people seem to have a hard time with this, the trick is that Patchy is really predictable. Wait for her to try to combo then shut her down. Particularly if you see her get a draw card in a Kourindou, prepare your counter.
Alice
You have the ability to turtle on top of permanents. Collect Focus cards and the Stopwatch and defend them. Save your bombs for cancelling Patchy's bomb.
Aya
A handful of Shoots and Grazes should be enough.
Byakuren
Do not use your Shoots on your turn, you shouldn't really be doing this anyway. Use your spell card when Patchy has the opportunity to drown you in Shoots to defend yourself, otherwise save Bombs for cancelling.
Cirno
Keep Patchy in range and freeze her when she picks up extra Shots per turn.
Eirin
Tank hits from Patchy a couple of times then heal yourself and possibly your team. You want to time things so that Patchy's combo fails and she's left herself overextended.
Futo
Give Patchy's hand to your ally, or anyone at all really. Even if you move it to someone on her team, they have to discard almost half of it at the end of your turn.
Keine
You're strong against Patchy. You can counter not only her spell card but all the draw cards she'll want to play.
Marisa
Borrow all her books. It's best if you sit on your shoots till you can play a lot at once.
Meiling
Use your spell card at the start of Patchy's combo (When she attacks after drawing or she just has a ton of cards in her hand)
Miko
You're really a team player, so you'll have to use your teammates. If your teammates follow you before Patchy, feed them the cards you can't use so you can team up on her.
Nitori
Anytime you play Nitori you want to be shooting off everyone's Power cards to make yourself invincible. If Patchy plays a Stopwatch or something do your best to negate it until you can get rid of it.
Reisen
Like all characters with a counter, you are strong against Patchy. Steal her spellcard and shut her down.
Remilia
As landlord, Patchy would be very unwise to attack you. Never discard a Graze and enjoy your overwhelming matchup advantage.
Reimu
Besides Aya, Patchy is best capable of doding your shots. However you can always ban Grazes, or Shots, or Sutra Scrolls.
Sakuya
One bomb and Patchy's combo ends immediately. Easy.
Sanae
Shoot at her a few times to fish for Grazes then blow Patchy up with the Miracle Fruit.
Satori
Combo Patchy before she combos you, remember to keep tabs on her hand.
Suika
You're probably one of the few characters who can out-tank Patchy and Nitori. It'll be a battle of attrition unless you can engineer a range advantage.
Tenshi
Let her hit you, feels good man. Challenge her to get rid of those Shoots.
Utsuho
You'll have to either survive a combo or strike when Patchy otherwise overextends herself. You've got great offense but you're a one trick bird.
Youmu
You have no particular advantages to utilize against Patchy, it's best to save your bomb to cancel hers.
Yukari
Like Remilia, you have a good matchup advantage going on, abuse it.
Yuuka
Don't use your spell card, you're weak VS Patchy so I'm afraid you have a rough road ahead.
Edit: Sakuya I haven't personally seen played since AX back in August, when I was playing as Patchouli and got my turn ended immediately after playing Voile.