Reincarnation is the spiritual successor and much more improved version of breeding in Pokemon. Its purpose is to improve the stats ranks (IVs) of your Puppets and to change the Puppet's emblems (Nature) as well. Reincarnation will be made available to the player once they have cleared the game once. It's done at the Scarlet Devil Mansion in the Library. When the reincarnation process is done, the Puppet is reset to normal style at level 1 with default skills.
How it Works
Using this wonderful Ruukoto & Mimi-chan as an example, You can see that it has terrible IVs. With IVs this bad you might as well go to Youkai Mountain and have Hina release this Puppet... but have no fear. Reincarnation can dramatically improve this terrible Puppet and transform it into a superior elite that will give this impure world retribution, all with ease. Jokes aside, since you're probably gonna be playing anonymous people online, it is expected that your dolls have 5/6 S ranked stats depending on what your Puppet is going for.
So first you must have two parent Puppets.
These two Puppets will be the key to fixing this very inferior Ruukoto & Mimi-chan.
The first slot is for the Puppet that wants to be improved. The 2nd/3rd slots are for the Puppets that will be having their stats copied over.
The 4th slot is the Mark Item slot. After speaking with Patchy in the library, she will hand you these items. These items cannot be sold nor can they be discarded. So you never have to worry about losing them.
There are a total of five marks, each of them affecting your individual stats like natures in Pokemon. However, unlike Pokemon, these natures come with no negative effects. Pretty cool right? What each mark does is as followed:
Red Mark: +10% Focused Attack
Blue Mark: +10% Focused Defense
Black Mark: +10% Spread Attack
White Mark: +10% Spread Defense
Green Mark: +10% Speed
The 5th slot is for Magic Stones. There are eight in total, and each other changes how the IVs are distributed between the donors and the recipient.
Note that the only puppet being affected is the recipient, and the donors are basically unaffected by the process. What each magic stone does is as follows:
Nothing: Obviously not a stone, but when you reincarnate without a magic stone, three ranks are chosen at random between the donors to be copied over to the recipient, with the rest of the stats being completely randomized.
Omega Stone: All of its stats stay the same, ignoring the donors. Use this if you only want to change the Puppet's Mark or the Puppet's style.
Gold Stone: The HP stat of the recipient remains the same, three other ranks are chosen at random between the donors with the rest of stat ranks being randomized.
Red Stone: The Focus Attack stat of the recipient remains the same; three other ranks are chosen at random between the donors with the rest of stat ranks being randomized.
Blue Stone: The Focus Defense stat of the recipient remains the same; three other ranks are chosen at random between the donors with the rest of stat ranks being randomized.
Black Stone: The Spread Attack stat of the recipient remains the same; three other ranks are chosen at random between the donors with the rest of stat ranks being randomized.
White Stone: The Spread Defense stat of the recipient remains the same; three other ranks are chosen at random between the donors with the rest of stat ranks being randomized.
Green Stone: The Speed stat of the recipient remains the same; three other ranks are chosen at random between the donors with the rest of stat ranks being randomized.
Rainbow Stone: One rank is chosen at random and randomized, while the rest of the recipient's stats are chosen from the donors.
Where to get the Stones
The Omega stone will be first given to you when try reincarnation for the first time. Gold-Green are found in the Ice Cavern (Post-Game), and the Rainbow Stone is given to you when complete the sidequest given by Kasen.
How to Complete the Kasen Sidequest:
Kasen's house is located on Youkai Mountain. If you have the Gap Map (you should really have it, if you don't I feel sorry for you), teleport to the rest stop on Youkai Mountain and head west. If you just continue west, you should see a sign that tells you're heading toward the Giant Toad's Pond. This is the right way. You should be in an area covered in mist now. Just explore around a little, but you should eventually find her house. Once you find her house, go in and talk to her. She will give you a quest to find four items of hers that were stolen and and displaced by the Three Fairies of Light. Time for some chores!
Peach Hairpin: Look for the Great Toad's Pond on Youkai Mountain (not that far from Kasen's house). A frog has one of the items near the north part of the map.
Monkey Seat: Go to Muenzuka. It's right in front of the large purple tree.
Dog Flute: Go to the Hakurei Shrine and look for a well behind it. Before the item appears however, you must defeat Shinmyoumaru, whom is located in the shrine.
Hochodo Book: Head to the cave behind the Myouren Temple. Once you find the item, Seiga will appear and battle you.
Get all four of these items and gap back to Kasen. Now you have the Rainbow Stone!
Here's what Ruukoto & Mimi-chan looks like after using the Rainbow Stone:
As you can tell by the image, this Puppet has certainly improved! The HP, Focus Defense, Spread Attack and Spread Defense were inherited from Kogasa. The Speed was inherited from Sariel, and the Focus Attack was the re-roll stat.
With smart planning and lucky catching, you too can get a full S ranked Puppet. It is recommended that you have at least two full S ranked puppets. There's a 1/16 chance of getting an All S ranked Puppet with both donors having full S ranked stats.
Now is for the final topic: Magical Fragments.
You've been getting these fragments all throughout the game, and you likely noticed that you've been obtaining many of these magical fragments. You might even have 255 of these. Well if you could guess already, each time you reincarnate it will cost you one MagFrag. You can easily waste away MagFrags through the grind of reincarnation, but fortunately there's a legitimate way to obtain more MagFrags for reincarnation: Online Battles. You can obtain a maximum of 6 MagFrags per battle, so hopefully you'll have a nice guy that can battle you and you can grind together. Be sure to try your best at preserving these items. (Otherwise you could use Cheat Engine)