Insane Difficulty: Final Fantasy VIII - Requiem v1.2.1 - Insane Difficulty

HP-J from Ifrit allowed me to junction cure to Squall's HP, giving him just enough to survive two attacks from Elvoret. Because of this, I was able to get double on Squall and have him on standby to heal whoever got hit during the battle. Once Squall was safely set up, I got a double off on Selphie, too. Then it was just a matter of Selphie and Squall always on standby to heal, and Zell sitting around with blind on waiting to get a duel off. I was also able to get off a Wall with Selphie, which, even though it cuts my healing in half, it lets me stay at lower HP to get limits easier. It took three 4 second duels and two 6 second duels to take him out. I would have liked to have drawn a couple doubles, but I didn't feel safe enough to do so (though I probably could have after I got a Wall off with Selphie).

Bite bugs inflicting poison is a nice way to make them remotely dangerous, though a bit annoying given the limited ways available to cure it at the beginning of the game. I like it.
Went straight to Fire Cavern, chose 30 minutes because I wasn't sure what to expect.
Ifrit was less of a pushover than normal. Used all 4 phoenix downs. Renzo spam with Quistis on healing duties was my tried-and-true strategy. Finished with 14 minutes left (Oh no, my seed rank). A quick scan of Ifrit showed 2500+ HP, which was a nice ~2.5 HP multiplier.
Anacondaur battle was intense. It hits hard and fast and had a lot of HP. Burned through four PDs (sold Occult Fan and bought 20). Put in an L4 and L3 Renzo and a few No Mercy's and the thing was still standing to my surprise. Got to the point where I had Zell and Seifer dead, Squall with 80 HP. I knew if I used a PD on someone I'd be done for since it was so fast, so I went for one last Renzo and prayed. Thankfully, it finally dropped from an L4 Renzo.

Elvoret destroyed me. Then again. And several more times. I really, really didn't want to grind (I hadn't done any card playing or grinding yet, and hadn't learned anything besides Card and I Mag Ref which is habit from normally grinding for some waters on the beach), but I saw no other option. Got an extra level and HP-J for Ifrit and was able to beat him on first try by keeping everyone healed and using Duel.
X-ATM was much easier...maybe even too easy. He doesn't hit particularly hard or fast. I didn't even try to beat him for the AP, since I didn't have the damage capabilities.
Granaldo wasn't too bad. Died on my first attempt because I wasted time trying to sleep him (I assume he's immune now) and failed a couple of times trying to cast protect. Second time I got the early protects off right away and it was smooth sailing for most of the fight. Once Granaldo was alone, it got a little more intense (since my protect ran out), but I had done enough damage to it while killing the Raldos that it went down with a few limits.

Diablo was a great surprise. Summoned him up, tried to get a blind off on him, and then saw him cast Death. Instantly stopped trying that, and just started spamming phoenix downs and limit breaks. I didn't notice any particular attack patterns, though maybe he started to use physical attacks as his HP got lower? Anyway, first attempt I feel like I did ~10k damage to him, but I ran out of phoenix downs. So I went ahead and got the 7AP needed for Siren's L Mag Ref, went and got Mini Mog, Zell, Quistis, and Seifer, and in the process got 100 death spells to hopefully block one of his attacks on Squall. I loved that you decreased the effects of status resistance.
For my second fight Diablos, the death resistance was useless (didn't block any of the 3 deaths cast on Squall), but I had the phoenix downs necessary to win. I didn't count closely enough, but it seemed like it took about 5 Renzos, 4 L1 and L2 duels, and then I was able to finish him off with an L4 duel. I probably should have scanned some of the bosses to check their HP, but I never bothered.

Fake president a pushover as usual, down with one 4 second duel. Then Gerogero owned me while I tried to stock up on doubles, thinking I could easily end the fight with an X-potion. Was nice that it healed him instead of killed him, though I should have expected it.
Second time around, I went with having Selphie and Squall on reviving/esuna duty while I tried to get Duels in. An 8 and 4 second duel and he went down like a sack of potatoes. Didn't draw the doubles that I wanted, but I don't think it'll matter. I think the difficulty was greatly improved, and should be a great fight after limits are nerfed (and if the player doesn't junction triples).

Lunatic pandora was less of a cakewalk than normal. Elastoids are dangerous, but the soldiers are boring as ever.

Brothers hit like trucks. Before I'd get my first turn, I'd have two characters dead. Throwing a PD is useless because of Mower. I tried a couple more times, but the fight was over before I would I even got a turn due to Mower hitting the whole party.
I decided it was time to upgrade my terrible junctions through some card playing (still refuse to mod the 180 triples, +60% str, or 3 auto hastes until I feel it's absolutely necessary) and learn some important stat-J abilities (namely HP-J from Diablos) so that I could actually survive some hits from Brothers. Just went for 300 regens and 100 Tornados, since I didn't want to grind too much.
My strategy was getting everyone set up with protect then double, and then keeping Selphie on standby while Squall and Zell attack Minotaur (the much bigger threat in the fight). Lost a couple more times to them, but then finally got a nice RNG where Minotaur attacked the person who I put protect on first, allowing me to get everyone in protect status before I got caught in a rez loop. Once everyone was set up and healed up, the fight went smoothly. Zell was doing quite a bit damage with a Tornado str junction and str+20% and +40% (84 str total) and aero on his elem-att. Once Minotaur went down, I took some time to draw some Lifes since Sacred is a wimp.

After you mentioned how hard Edea is, I considered making Lionheart, but decided against it since it would be extremely cheap and I hate grinding Elnoyle cards.
Anyway, on to the actual battles:

Iguions were a cakewalk. I have ~2300 HP at this point with Regen. Firaga and break junctioned to Squall's defenses makes him essentially immune to Magma breath, though even that was unnecessary since Irvine only took ~250 damage. Their claw strikes did about 300, and resonance about 500 (though they only got off one of those). Squall with Tornado on str, quake on elem att, and str+20% str+40% was doing about 900 damage a hit. Didn't even need to use limits or anything, just some old fashioned attacks while Irvine stocked up on Esunas and a Carbuncle.

Seifer got a nice boost (I see why you removed Vit0 in this patch - I wonder how hard the fight would be if he inflicted Vit0). Still not a difficult fight, but I don't think it should be since it's a 1-on-1 with little choice in strategy.

Edea was much easier than I expected after your warning. Casting meteor and death was better than having only reflectable magic, but the thing about meteor is that the damage is spread out over three members, making it unlikely to kill anyone on its own unless they were just revived. She's also quite slow and doesn't have much HP.
The first attempt, I think the battle just randomly ended after she casted meteor for a second time and Squall died. I'm pretty sure no one else died, but maybe I just imagined that Irvine and Rinoa lived. It's early in the morning -.-
Anyway, second attempt she went down with a C4, C2, then C3 Renzo with two fated circle finishers. Each Renzo hit did ~900 damage, so that puts her HP around 20k?
I think she could definitely use some speed, magic, or HP boost (or a bit of all 3). I get that you're planning on nerfing Renzo, but even then that would only serve to prolong the fight, not make it more difficult.

Modifying Mighty Guard. As it stands now, the effects of Mighty Guard are:
C1: Protect, Shell
C2: Protect, Shell, Regen, Haste, Float
C3: Protect, Shell, Regen, Haste, Float, Aura
C4: Protect, Shell, Regen, Haste, Float, Aura

There are a couple things about this. First, with Aura spell becoming more rare, I think that immediately increases the power of the otherwise useless Mighty Guard. One could even say that it's now TOO powerful. But, I think if you reduce the Aura modifier (I suggested 100 earlier) and take Aura out of C3, then you've got some nice abilities but not too easy to get Aura. Still, I think the jump from C1 to C2 is too much, and I also think having regen on mighty guard actually makes it worse (regen is one of the worst spells in the game, especially at lower levels when you would actually use mighty guard, and now even worse because of decreased junction effects for HP). So my suggestion for mighty guard would be the following spell set:
C1: Shell, Protect
C2: Shell, Protect, Float
C3: Shell, Protect, Float, Haste
C4: Shell, Protect, Float, Haste, Aura

I also thought about replacing float with double, but I think that Aura being so rare makes mighty guard powerful enough as is; also, it steps on Cerberus's toes a bit.

Just for fun, I went back to my save right before the Seifer/Edea battle and junctioned Triples/str+60%/Auto-haste. Squall has 130 strength (base of 30).
I killed Seifer with 4 hits of ~1200 damage each, with him getting only one attack in.
I made save state there to test Edea with and without limits.
With limits: two C2 Renzo's at 2k damage a hit ended the battle with her getting two turns.
Without limits: Just a slightly longer version of the fight with limits. Rinoa double casting Quake, Squall attacking, Irvine double casting cure/cura/curaga.

As an additional note, I got to see Edea cast flare this time (didn't see it in my original battles - also, she didn't cast death once this fight...is it just random or are there certain conditions for her casting certain spells?). Her flare is remarkably unimpressive. ~800 damage to a single character without shell. I assume that you can't increase the power of her Flare without also increasing the power of her Meteor though, right? If for some reason you can, I suggest that you do - by a lot. It should OHKO or nearly OHKO since it's single-target and can be reflected. You could then increase her spirit a lot more to compensate for her being with her own flares.

Another option for her would be to get rid of Meteor, increase her magic and spirit by a lot, then give her Tornado, Quake, and Flare (and death, though it's getting kind of annoying with every boss having death lol). Have it so Flare can OHKO (I had 2400 HP with HP+20 and Quake junction - the only better junctions at the time that aren't stupidly time consuming are Tornado and Pain, and those are just barely better...You can also grind for HP+40 and HP+80 with brothers, but that's also excessive) and Tornado and Quake can deal about 1500-2500 damage per cast to someone with Curaga on spirit junction (though it's worth noting you can only have two chars with spirit junctions at this point, so maybe that's a bit much - I'm not really sure how much spirit matters). Quake can be guarded by float and Tornado can be reduced by elem-def junction (technically everyone can have elem-def x2 at this point).

As another aside, I think this is a perfect time to consider reducing the effects of elem-def junctions even more. Completely nulling elements with ease reduces a lot of options for boss fights, since it makes no sense to give a boss an elemental attack if it can be easily guarded with one of four elemental defense slots. If you halve the elem-def of the spells again, then Tornado + aero would guard 70% of wind damage, and Quake + float would guard 62% (but casting float guards it 100%, so that's fine).

This would put Edea's Tornado casting at .3*2500=750 damage per player, which is about what Meteor was doing before. But everyone having elem-def x2 at that point requires a lot of extra grinding, so better to assume just elem-defx1 and put Tornados damage to around 2k. Then you've got Tornado doing 1000 damage per player with Tornado junctioned to elem def or 1600 damage per player with aero junctioned. Quake could still OHKO some party members without float, and Flare would OHKO anyone without reflect.

The battle doesn't need to be won, so it should be really hard. You could even increase the AP reward since 20 is pretty low if the fight is hard.

To make it even harder, you could not lower her spirit and instead substitute Holy for Flare and make her absorb Holy, so that if you reflect it back at her you heal her.

Not sure if you should increase her HP if you make her hit really hard. Low HP but hitting really hard could be a fun assassination-type battle where you just try to take her out before she takes you out. If you give her a lot more HP, it becomes a battle where you try to set up your party with float and maybe reflect, then grind her down while trying to stay alive. Both types of fights can be fun.