Apophis down:

After playing the game for over a year and spending thousands of dollars to get extra SS Memorias and limit breaks, I finally defeated the strongest boss in the game -- Anachrony Apophis.  I used two squads to fulfill the task, each with their own designated vital task:

My first squad was the 'shield' squad.  It fought Apophis for the first 155 turns or so.  Its job was to break Apophis, get Apophis' devastation rate to max 999%, and get my overdrive bar to max level 3.  Vritika and Chie were the core of my strategy, as they both had autoheal abilities that restore a percentage of your dp at the start of every turn, the only way to fight a boss that did so much damage per attack for an extended length of time.  (If you use active heals you'll run out.  Though of course I used Vritika and Chie's active heals too, until I was totally out of them.)  Assisting Vritika and Chie were Ichiko, Seika and Erika, three more defenders, for a total of 5 defenders in the same squad.  Seika would give everyone auto-crit with her Stardust Trajectory, and Erika would assist with her Angelic guard, provoke, and basic damage dealing when Vritika needed a break.  Ichiko's main task was to damage the boss, though all her abilities also raised the party's defense or lowered the enemy's attack, like a proper defender.

Assisting these 5 defenders was a single buffer, tuxedo Tsukasa.  Tuxedo Tsukasa can produce a fire and a light field, which could indefinitely cancel out Apophis' most dangerous ability, Sandstorm.  She also did a lot of damage, reduced the enemy's fire defense (which let Ichiko and Erika do more damage), and enhanced everyone's skill damage.  But Tsukasa was mainly meant to weaken the enemy's attack, the same as the 5 defenders she was working with.

By keeping Apophis' offense generally below the capabilities of my defense and autoheals, I was able to drag the fight out for the 155 turns required to put the boss in a vulnerable position.  I could have held out for a few more turns, but I was out of powerful heals so I figured it was time to move on to phase 2 of the fight -- i.e., squad 2 of the fight, the people designated to actually kill the boss.

Squad 2 consists of fox Miya, base Muua, samurai Inori, phantom thief Jamie, base Yingxia and pajamas Hisame.  Hisame fared poorly in this fight.  Her Munechika attack is too dangerous because it simultaneously lowers her defense by 100%.  Against a boss like Apophis that could have been lethal, so I couldn't actually utilize her true power.  The others worked as intended, though.

Muua also has the same autoheal ability as Chie, and she's an actual healer so she had some active powerful healing skills as well.  Her job was to keep my lethality squad alive for the ten turns they needed to bring Apophis' health bar from basically full to nil.

Fox Miya can produce light fields, so her job was to counter Sandstorm in case Apophis cast it again.  As it turns out Apophis didn't cast it again, so Miya just concentrated on debuffing the boss, which multiplied the damage Jamie and Inori could do.

Yingxia's job was to buff Inori so that she could unleash her ultimate attack, Tadamusa, in its ultimate form.  She performed that job exquisitely, but she also managed to buff a few other people and debuff the boss for that little extra bit of damage.  Yingxia really is one of the strongest characters in the game.

Jamie's job was to hit the boss as hard as she could with her critical penetration technique, but she also gave extra sp to Yingxia so she could buff Inori faster.  Jamie did a lot of damage, but it was still nothing compared to Inori.

Inori's job was to kill the boss with two swings of her mighty Tadamusa blade.  I'm afraid to even say how much damage she was doing because I feel I must have read it wrong.  Either it was 23 million damage a swing or. . .230 million damage. . .  And still it took two swings.  She can use Tadamusa 4 times, but honestly Muua couldn't have kept the party alive long enough for her to use the technique all 4 times, so it was either those two shots or bust.

Looking back it would have been better to use an extra healer instead of Hisame in the kill squad, but *shrug*, who cares, it worked!  And this way my beloved Hisame can claim she helped defeat the game's last boss.

Apophis isn't actually the last boss though, there's another Anachrony called Skullfeather that I have to beat next.  But according to all reports, it's much weaker than Apophis, so next week when I get my next anachrony pass (that gives me the right to challenge an anachrony boss), I'll truly defeat the game by taking Skullfeather down too.

What perfect timing.  Right before the new year, I'll clear the entire Heaven Burns Red game, defeating every last boss it threw at me.  And of the 12 Seraphs who brought Apophis down, only Tsukasa was from Squad 31-A (the main characters of the story).  I went way off the beaten path and used a very eclectic mix that no sane person would have put together for a boss fight.  But I saw a path to victory using autoheals, using defenders and healers in the first half -- and critical penetration attacks in the second half.  And after trying and failing to beat Apophis in a fair fight for months and months, this was the only path I could see.  I've been building my troops up for this moment, for this solitary path to victory, for months.  At least for fights like Apophis with no time limits, autoheal and critical penetration are the best abilities in the game.

Now that I've defeated Apophis maybe I won't have to spend any more money on the game.  It can be played for free, so long as you're willing to not get remotely as strong as fast as before.  I felt like I was desperately playing catchup until now, because I couldn't beat Apophis.  But now that I can beat Apophis, I can coast from here and still be strong enough to handle anything the game throws at me.  It's like reaching the peak of the mountain.  The rest of the game is all downhill.  I'm already stronger than the game thinks I am, so none of its remaining challenges will faze me.  I'm finally ahead of the curve.

God I hope Skullfeather isn't somehow harder than Apophis. . .that would ruin everything I've worked for up until now. . .  I guess we'll see next week. . .  One more fight and I'm free and clear. . .