“Sakuya, you came earlier than I thought.”
“As I thought, Miss Patchouli is here.” So this is the powerful witch Akyuu mentioned.
“Since you’re here, let’s have some fun.”
“I don’t mind, but is your health okay?”
“There’s nothing to worry about. Today is a good day. I will show you a bit of my true magic powers…”
Patchouli is a difficult boss fight because she is another flying enemy and has a lot of attacks that can make Sakuya’s power useless. As long as you dodge well and find places to attack her, you should be fine. For her first attack, she flies up to the top of the room and throws spears of water down at you. This mimics the original Touhou games because they’re a bit scattered and you can dodge them if you move around to spaces where there isn’t a spear. You can also use the sliding knife to get to farther away spaces to dodge. If you try to run away from this, Patchouli speeds up to get to your location.
Her next attack is slightly targeted to you. The books she summoned glow red to signal this attack. Each book she has will produce a large ball of fire. Each fireball can turn once in your direction. As long as you find the way to get around them, you shouldn’t get hit.
This next attack is especially hard to dodge. She creates balls of water and throws them down. They will be turned in your direction. This seems manageable, but Patchouli also creates waterfalls on the outside. You will get stuck on these if you try to stop time and you can’t escape this by running away because Patchouli is faster than you. Since the water she throws goes in your direction, it will eventually be impossible to run from. You need to get to the other side of the water she is throwing. You can do this during the slight pause after she throws one, but if it seems to hard you can use the sliding knife to help. You can also pause or slow time to get to the other side because the waterfalls aren’t blocking the middle.
Patchouli’s books glow green. She moves to the floor. Out of each of her books come around eight green danmaku.
She also summons an additional eight from her hands. This is not really an attack but rather a block she sets up. These green danmaku also have a green aura. If you pause time, they will all go flying and hit you. This is especially annoying because the next attack is very hard to dodge without time paused. Her books glow white and a large dragon comes out of each one. They speed up and fly in your direction. If you get the opposite direction they fly in, they will try to readjust and get to your position. Since they can’t stop, they will slow down trying to turn and likely fly out of the screen before the can hit you. Since you will need to pause time to get to the opposite direction, the block can cause you to fail and take a lot of damage doing so. You can either slow time to get past the dragons or before they are summoned, slide under the green danmaku to the other side. That way, when you pause time, they will all go flying a direction that won’t hurt you. You can then deal with the dragons however you like. 
Patchouli then flies to the ground again and throws large rocks. The explode into smaller rocks when they hit the ground. They hurt no matter what size they are, so don’t touch the rocks. This attack can seem to box you into a corner. Stopping and slowing time could be used here, but another method of dodging them is better because it will deal damage as well. This method is the Thousand Dagger you got earlier. As mentioned in the stage three guide, the Thousand Dagger makes you invincible for its duration. Since Patchouli is at your level for this attack, it is easier to hit her with this skill. Although the Thousand Dagger is very powerful and a great skill, it has some incredible aiming difficulties to go with it. The Thousand Dagger can only be aimed at a slight angle above you when the enemy is far enough or directly in front of you to the direction you are facing. Be mindful of this as you use the skill because it would be a huge waste of a lot of MP if you aimed incorrectly and didn’t hit anything.
Patchouli flies back to the top and creates lines of fire. They start in a center circle and expand outwards, so for this attack you can dodge it by staying directly underneath her. This is the last attack in her attack cycle. Attack her until she has low health. For dealing damage to Patchouli in this battle, things can become complicated as some of Patchouli’s attacks don’t allow for breaks to throw knives. You can always do something in between Patchouli’s attacks as she adjusts to a different position. Her first attack where she throws water spears is very difficult to dodge and throw knives at the same time, so the only thing you can do safely is using Auto Aim. For the fireballs she throws, you can simply stay directly under her and throw knives upwards. They are significantly easier to dodge, so getting out of the way of the fireballs while attacking should be no problem.
The next attack where she throws water can be hard to dodge and throw knives similar to the water spears. Your only option here is Auto Aim again. After this, don’t use any MP. I know she is more out in the open for the next three attacks, but you want to conserve MP right now. Just deal with the green damaku and dragons. If you get a chance, you can rapidly double jump for a short while to recover MP when you pick up the knives from it. She then flies down to Sakuya’s level and throws rocks. Now use the MP you recovered to use Thousand Daggers. Continue attacking this way until Patchouli has low health.
“Well done… How about this?” It’s Patchouli’s final spellcard! Except… It’s not a spellcard? Patchouli summons two more books. Uh oh… Instead of a final high damage spellcard, Patchouli adds two more books and modifies all her attacks to be stronger and harder to dodge. This could mean trouble. The water spears stay the same mostly, there are just more of them and they’re thrown in a wider range. If you continue dodging the way you did before, you should be fine. 
Now she throws four fireballs. This can become harder to dodge, but as long as you don’t stay in the same place for too long, none should hit you. The attack where she throws water danmaku and creates waterfalls around changes slightly. Now there are also water danmaku on the sides along with the waterfalls. You can still get around this the same as before, it’s just definitely impossible to escape this now. The green danmaku never hit you, they just go around you so although there are more now, you can still easily get rid of them in the same way. What is difficult now is the dragons. Try to position yourself on far end of the room after getting rid of the green danmaku. Now four dragons come flying at you. If you wait for them to almost touch you and then pause time to get to the other far side of the room, they should all fail at turning and fly off screen. Great! Now hurry back to Patchouli’s position and stand underneath her. The fire circle is similar, but now that there are more lines of fire there is no way to dodge them if you aren’t directly under Patchouli. You have to jump over a small line now in the center. The cycle repeats. Continue attacking Patchouli until she is defeated.
“Cough!! Cough! Ugh… My asthma. When I least need it!!”
“I’m sorry. Without thinking, I went all out…”
“Cough. Cough. Don’t apologize, it was fun. I’m surprised you could use your powers though. We should have sealed them. Did you break the seal by force?”
“This is thanks to a gadget loving kappa. Personally, I don’t like depending on tools, but…”
“…? Remi left quite a useful character for you. No… That’s not it. My intuition was right. I had a bad feeling, so I made it rain… But to use gadgets… She’s pretty smart, too…”
“Miss Patchouli?”
“Oh, nothing. It’s nothing. Anyways, you won so you can move on. “
“Will I be able to see Lady Remilia soon?”
“Yes, she’s waiting at the clock tower just past here. Since it’s Remi we’re talking about, I’m sure she’s itching to play with you.”
“After Miss Patchouli, I can’t let Lady Remilia wait. Oh, Miss Patchouli, please go home and rest.”
“Yes, I will head back to Scarlet Devil Mansion first… The real one.” Patchouli flies out of the room and leaves the scene. 
“As I thought, it was Miss Patchouli who created this world... Next is Lady Remilia at last. I must hurry to Lady Remilia to escape this world as soon as possible.” Everyone seems to be acting odd in this stage. What about Nitori using gadgets to get past rain? She always uses gadgets, she loves them. Patchouli must have been referring to the mech that took off in the rain during stage one that Nitori gets around in. Is she not a fake? The conversation with Patchouli raises more questions than answers.
Go to the room in the right and get the key. Now you can go to the left and go back the way you came. Once exiting the hallway, go up using grip knives. There is a secret room to the right. Once you’ve collected the item, go to the left. Stage four should be the last. You can soon be released from this world.