Hmmm... impossible you say...
Well, I guess here's my cheap thoughts from a purely theoretical standpoint.
Let's assume for a start that Sx is no object, so you can go into the war with all the equipment your little munchkiny heart can desire. Let's note down Fuzkao's abilities and stats so much as we care about them. The first thing to note is that his skills can't inflict status ailments, so you are free to swap out your various pins for items that increase attack or magic, if applicable. Fuzkao has a DEF score of 125 and a MDF score of 200 in the fight we're talking about. He is vulnerable to debuffs of DEF and magic MDF. His elemental weaknesses are anti-sex and ice at 125%. Physical attacks hit him normally. He's 50% resistant to sex.
So since we are interested in inflicting as much damage as fast as possible, our first choice is obviously going to be Varia. We're going to give her the crusader sword in place of one of her custom swords, and equip her with a ring of strength from Stenai. (Although you might argue for heirloom pin II if luck increases the odds of criticals.) You'll want to give her an assault helm in preference to a sublime helm for the extra ATK score but sublime armor is better than assault armor in just about every category. You can make a case for crusader armor for the slight increase of ATK in exchange for the higher probability of Fuzkao knocking Varia out of the fight. Breastplate de Iris with elemental resistance might be optimal, but I can't see you making it just for this fight.
Varia is going to spam blade dance and should do a healthy amount of damage.
Slot #2 is also a forced choice: Vhala. We're going to have her spam arrow of abstinence, which attacks MDF instead of DEF but combines ATK and MAG stats to do so. So the lean or massive unbow are the weapon of choice since the extra MAG more than makes up for the lower ATK these have in preference to the desert unbow. Ring of strength is also a no brainer. Assault helm is a no go here because the increase in ATK is offset by the decrease in MAG. Likewise, mammoth helm is out. Sublime helm is the only choice. Sanctity plate is good if you have it, but the optimal choice is probably savant's cloak, with the hope that the helm provides enough defense. Tormented shield may look tempting, but the additional ATK is more than offset by the lower MAG. Archer's gloves is best if you still have it, followed by sylvan gauntlet. Breastplate de Iris with elemental resistance is also an option, but again you're not likely to get for just this battle.
Simon's attack of choice will be either precise strike or incubus strike depending on SP availability. Incubus strike will do slightly more damage. Both are based purely on ATK, so sublime sword, assault helm and ring of strength are mandatory. Assault armor and sublime armor confer no advantage over lustplate in this case. The big question is "incubus glove or tormented shield". The tormented shield will greatly increase Simon's damage output, but it will also render support allies impotent in terms of hp restoration. Since Simon is probably going to be the only way you have of keeping the party standing, eliminating his healing capability is a big risk.
Robin is probably the most sensible 4th party member spamming ice lance, with the flexibility to use healing lance in case Varia needs it. You can make an argument that Riala or Altina might be a better choice because it's easier to get their MAG skills higher with sexual equipment (such as the greater magic necklace), but ice is blocked better by a high MDF than ice lance (and Fuzkao has a 200 MDF). Roughly speaking, Robin will do 1.5x as much damage with ice lance for each additional MAG point as Riala and Altina will do with just ice. (Storm of lust is a sucker play here.) The optimal loadout for Robin is probably sublime staff or assault rod, sublime sphere (although the arcane crystal is not much worse), unperson circlet, crusader robe and crusader charm II.
I'd suggest another option for the 4th player though, with two strategies and two loadouts: Ginasta. You can either maximize ATK and use tyrant slayer every round, or you can maximize LUK and use suppressing strike the first two turns to make everyone else hit harder followed by tyrant slayer. With either strategy, sublime sword, assault helm and Erosian priestess robe are your preferred equipment... Stop laughing, it has a ridiculously high +40 ATK bonus AND +100 LUK in addition to +30 AGI and respectable defense. If you are maxing ATK you once again need to use ring of strength, and top it off with tormented shield. For the maximum LUK build, you want heirloom pin II and then sylvan gauntlet is your best choice for off hand, followed by thug's orb. You probably need the net +200 LUK bonus to reliably apply the debuffs to Fuzkao. This raises the question of why we're not using Aka to do this, since she has a naturally higher LUK. The answer is that Ginasta's suppressing strike does a bit more damage than aka's disabling strike, tyrant slayer does significantly more damage per ATK point than ecstatic strike and much much more than forceful lunge, and we can boost Ginasta to a slightly higher ATK score. These aren't overwhelming reasons though, and you can probably use Aka with a sensible equipment loadout and heirloom pin II to roughly the same effect.
Hope these ideas help.