To upgrade your P-Organ, you need Quartz which can be found throughout the game, and can be used by going to the chair in Geppetto's office to obtain skills. You'll need to unlock a certain number of large nodes before the next phase unlocks. There is a finite amount you can obtain, but you can obtain them again in New Game+, and also unlock an additional phase 6, and phase 7 in NG++.
None are missable, except the Quart from the Broken Puppet NPC who is next to the Barren Swamp Stargazer, if you don't have the Gestures, Clap, Sad, Anger, and Happy. Here's my other guide on where to find them! (You can come back after obtaining them)
The list was created by PowerPyx, but I have corrected some errors and included the missing Quartz from the original guide.
You can teleport to the listed nearest Stargazer to quickly find the Quartz. A few of them will need to be bought from Polendina’s shop at Hotel Krat after finding a Sturdy Krat Supply Box. Give them to Polendina and he will have new items to buy which include a Quart. (1 Quart for each box)
11/14/23 - Version 1.3.0.0 - In this new update, you can now obtain 3 more quartz! Increasing the number of Quartz you can obtain in a playthrough from 28 to 31!
"2 more Quartz can be purchased during the early stages of the game.
After expanding the shop for the 1st time, 1 additional 'Quartz' can be purchased. (Yes, 1 more Quartz.)"
There is a total of 31 Quartz that can be found! Make sure to obtain them again in New Game+! Cerasani Alley1. Dropped by the Parade Master boss. (Main Boss)
Krat City Hall2. Dropped by the Scrapped Watchman. (Main Boss)
Workshop Union Entrance3. Dropped by Puppet of the Future boss. At the stargazer, there is a path on the left side. In the end, you can drop down using the ladder. (Optional Boss)
Workshop Union Culvert4. From the Stargazer, go through the tunnel with the rolling ball of fire and you will eventually come across the Red Fox and the Black Cat. Continue past them and head right when you come to the split with the big red pipe. You’ll eventually find a green door on your right you can unlock using the Trinity Key you can acquire by solving the King of Riddles’ riddle found shortly after Krat City Hall Courtyard. Enter the room and rip the safe open.
St. Frangelico Cathedral Chapel5. After dropping the brazier that dispels the Decay at the bottom of the tower, continue on to find a cell doll you can open. Defeat the Elite enemy that drops into the room.
Inside the House on Elysion Boulevard6. When you reach the top of the wooden tower at St. Frangelico Cathedral Chapel, kick down the brazier to dispel the Decay pool on the ground floor. Then, access the underground chamber and pick up the Crafted Cryptic Vessel. Head back to Hotel Krat and talk to Venigni to have him decrypt the Cryptic Vessel.
The first decryption leads to an assignment: you need to strike the puppet that hangs from the Alchemist Bridge on Elysion Boulevard. To do so, fast travel to Krat City Hall stargazer and walk back. Throw a sawtoothed wheel at the puppet to drop the second clue.
The second clue is Letter with the Refuge’s Address with a photo of the location you need to find. Head back to the Krat City Hall stargazer and teleport to Inside the House on Elysion Boulevard stargazer. Now leave the house and cross the beam. The correct door is on your immediate right before the puppets. Open the door and rip the safe open to obtain the Quartz.
Malum District7. You’ll eventually reach a square with many enemies (has a large Elite enemy patrolling in a circle), with some Decay-throwing ones on the upper ledges. This Quartz is found in the chest inside the open building in the middle with the destructible crates blocking the way (you can also drop down from the hole in the roof).
Malum District Town Hall8. After defeating the Eldest of the Black Rabbit Brotherhood, inside the hideout, in a chest behind the counter. (Main Boss)
Rosa Isabelle Street Culvert9. From the Stargazer, drop down into the sewers and you’ll soon reach a fork. At the fork, go straight on and drop down into the hole below to land on an enemy. Follow the pipe to eventually find the chest. You can then use the ladder to open a shortcut back to the most recent Stargazer. Drop back down into the sewers and now at the fork take the pipe leading up and out.
10. Dropped by the Elite Mad Clown boss that is on the staircase to Estella Opera House. For an easier fight, run-pass all enemies on the way and the clown and activate the stargazer up the stairs just past the clown. Then you can aggro and only fight the boss. (Optional Boss)
Hotel Krat11. Can be bought at Polendina’s shop after expanding his shop via the Sturdy Krat Supply Box you find at Grand Exhibition Gallery. The Sturdy Krat Supply Box can be found inside a chest near the shortcut ladder back to the Stargazer.
Estella Opera House Entrance12. In the same room with the swinging chandelier. Drop down and behind your is a Trinity Sanctum. To access it you need the Trinity Key obtained by solving the riddle that the King of Riddles’ riddle gives you at the Grand Exhibition Gallery gives you. Return here when you have it. The answer is Candle.
Grand Exhibition Gallery 13. In a chest outside of the gallery. While going through the gallery you will find a section that leads outside to a balcony. Go down the ladder on the left side and you'll find the chest next to the wall to the top right.
Barren Swamp14. At the Stargazer, talk to the Broken Puppet. He wants you to show him certain Gestures. Show them all for the Quartz.
15. Dropped by one Puppet of the Future. (Optional Boss)
16. Dropped by the other Puppet of the Future. (Optional Boss)
Krat Central Station Platform17. From the Stargazer, drop down on your left into the decayed area to find the chest containing this item. Make sure you destroy the fungus controlling the Decay.
Hotel Krat
18. Can be bought from Polendina’s shop after returning the Special Krat Supply Box you found at Collapsed Workshop Tower. The Special Krat Supply Box can be found after near two fire-spitting puppets. After going through the house with the swordsmen and reaching the rooftop, continue down where a second fire-spitting puppet is. Continue past him to find the Supply Box in a chest.
Barren Swamp Bridge – Hermit’s Cave19. Talk to Hugo by the gate behind the Stargazer. He will talk to you about how bad he wants to go through the gate. When he’s done talking, exhaust his dialogs to get the two items. You can now take the Cryptic Vessel back to Venigni at Hotel Krat. Once you’ve obtained the Special Krat Supply Box at Collapsed Workshop Tower later in the game (see below), hand it in at Polendina’s shop and buy Rusty Cryptic Vessel. Then, hand it in to Venigni and come back here. The gate will now be open. After dropping a second hole in a rooftop, you’ll find this in a chest.
20. At the very end of the cave, inside the safe.
Krat Central Station Street21. Obtained for defeating the Corrupted Parade Master. (Main boss)
Relic of Trismegistus Entrance22. Obtained for defeating the Black Rabbit Brotherhood. (Main boss)
Arche Abbey Outer Wall23. When you reach the room with the two beams in the middle, continue down to the bottom floor to find the last Trinity Sanctum. To access it, you must have opened all previous Trinity Sanctums and obtained the last Trinity Key by interacting with the telephone one last time near the Krat Central Station Street stargazer. Refer to Lies of P All King of Riddles Locations and Solutions if needed. Once inside, speak with Arlecchino and you’ll obtain this item regardless of whether you lie or tell the truth.
Arche Abbey Broken Rift24. Dropped by the Elite enemy, a large wooden Pinocchio toy you find in your path at the ladder.
25. At some point, you’ll reach an area with two big swordsmen on some stairs. After the second big swordsman, drop down the next ladder you see. From here, take the side path and carefully make your way across the traps. Weapon up as there is a Gatling gun enemy on the other side.
Abandoned Apartment26. While visiting Arche Abbey Broken Rift, you’ll get to an inner foggy area. After climbing up a ladder, you’ll be at a fork with a Harlequin elite on your left. Go straight on instead and then left where an enemy is protecting a chest containing this item. Now head back to Hotel Krat and hand the Cryptic Vessel to Venigni.
To solve this, head to Abandoned Apartment stargazer. Go up the stairs and leave the building. Cross the sign, but don’t go through the gate, instead flank the chasm and walk across the small piece of rock. Then, after the piece of rock, go right and left into the street. Climb the furthermost staircases. Equip the Frozen Feast weapon (bought in exchange of Reborn Champion’s Ergo dropped by Champion Victor main boss) and talk to the Wandering Merchant to get the Quartz.
Ascension Bridge
27. When you reach the Elite screaming enemy, you’ll find a chest containing the Quartz.
Arche Abbey Upper Part – Internal Bridge28. Dropped by an elite Disruption enemy you find in your path.