Ar Ru (boss)
The physical manifestation of the Antibody Brain, the Will of Ar Ciel that controls and creates the Antibodies. Despite her rather cute look and small body, Ar Ru is quite fearsome: she is always accompanied by some Antibodies, and has pretty strong attacks. You will face her a total of three times, all of them in visits to Moocheriel.
First Battle
This is the battle at the end of Phase 3 in the True and Bad Routes, where Aoto interrupts Saki's singing of EXEC_FLIP_ARPHAGE/., which in turn allows Ar Ru to fully possess Finnel and use her body to begin singing EXEC_ViiBaCi_MjiiRa/., which activates Moocheriel and forces it to mass produce Antibodies. As you might be guessing, ViiBaCii MjiiRa will be background music for this battle.
Ar Ru has only a couple of attacks, but one of them is an unavoidable explosion directed to one of your characters and the other one is generating an energy field around of herself, both of which cause tremendous damage, are very hard to block, and to make matters worse, can inflict all status ailments on the characters they hit. Ar Ru herself is very speedy too, so you will always have to be on your toes to be able to protect your Reyvateil properly, as otherwise Ar Ru will most likely kill her with just one attack. And as if this wasn't bad enough, Ar Ru also has access to a Stored Attack: Ar Ru I Love Therefore I Destroy, which produces a massive explosion that causes tremendous damage to all party members and also reduces their defenses, so if you aren't able to interrupt it and your stats aren't high enough, this will cause you a Game Over.
To defeat her, make sure to first Purge the Hyumas that increase healing amount and defense to give yourself better chances to survive her attacks, and carry lots of healing and revival items. If you can manage to survive until you can unleash a Flipsphere or several Ultra Supermoves, you will win this battle.
Finally, don't pay much attention to the Furia Model I that also appears in this battle, as its the most basic of all the Antibody monsters and shouldn't cause you much trouble.
Second Battle
This battle will take place in Phase 4 after EXEC_COSMOFLIPS/. has been Downloaded into Tyria, who tries singing it to convince Ar Ru to fuse with her and put an end to the threat of the Antibodies. However, Ar Ru declines the offer and instead tries to annihilate the party, so Tyria asks them to protect her while she sings.
This battle is a hopeless one in which you are expected to lose, so don't bother doing anything: Ar Ru has massive defense and is completely immune to all forms of attack, so you won't be able to deal even one point of damage to her. Furthermore, her attack power was increased to the point in which all her attacks can instantly kill all party members, and once she uses her Stored Attack, your entire party will be dead, so just allow yourself to lose to proceed with the plot.
However, there is a way of defeating her: the Ar tornado bombs, dropped by the Doll Carrier Type Hs found at the XP Shell, can pierce her impenetrable defenses and deal large amounts of damage to her, so if you manage to get some, you can defeat her. However, your only reward for doing so will be adding her invincible form to the bestiary, as the events of the game will proceed as if you had lost.
Final Battle
This battle will take place after Aoto tries Diving into Finnel to reach Ar Ru and convince her that humans still deserve a chance, prompting Saki and the personae of both her and Finnel to create a special Song Magic to convey their feelings without harming her.
For this battle, Ar Ru had a large increase in her attack, making her one of the enemies with the highest attack in the entire game, so if you don't pay attention, you will get your entire party flattened by her in no time. And if that wasn't bad enough, the Doll Model HBL Antibodies accompanying her can use the Forced Purge skill, which means that you will get your Burst Gauge charge and Song Magic wasted if they manage to unleash it.
Therefore, your priority aside of maintaining your party alive should be eliminating these Antibodies first, which you should be able to do easily if you can charge your Song Magic to around 20000% while having your Reyvateil at Purge Lv. 4. After that, defeating Ar Ru should be much easier, as her resistance to Thunder and all ailments were greatly reduced, and surrounding her with your Vanguards should greatly speed things up.
Finally, as you might have noticed from the conversations, all the Reyvateils and personae will have their standard Song Magic replaced with an special one that has a circular target area. Likewise, their Flipspheres are replaced with a rain of rainbow-colored energy spheres, both of which represent the sending of feelings.