Minerva is at level 100 and has 10,000,000 HP and 999,999 MP. She uses non-elemental attacks, the strongest being Judgment Arrow, an attack with animations resembling that of a summon. Her special move is Judgment Arrow that greatly depletes the player's HP, takes away their MP and AP and nullifies buffs (including Reraise).
Once she is defeated, the player obtains the accessory Divine Slayer, which increases HP, MP and AP by +100%, and increases all stats +50, breaks the HP, MP, AP, and damage limits, and gives Auto-Libra.
The player can repeat the battle even after she is defeated.
Costly Punch method
Zack will need to be able to break the damage limit. One strategy is to use a Costly Punch Materia, which will deal a maximum of 99,999 damage (if the player only uses Costly Punch it will take 101 hits to win). Other materia to equip include a Full Cure/Curaga, Phoenix Downs, Elixirs, Somas, and Ethers.
It would be recommended that as soon as the player sees Judgment Arrow, they switch to Ether, and select it so that Zack can restore his MP and use Full Cure. It is also advised to have Zack equipped with a Phoenix Down, and if he uses that one, Mug more from Minerva. It is not worth equipping a Libra because Minerva's HP and MP are hidden due to being so high. Even with a full set of Genji equipment, Ziedrich, and materia with high stat boosts, this fight can be very difficult.
The player should not recklessly press on Costly Punch, because it won't make Zack's attacks come any faster, and he might need to switch to dodge roll or guard. If Zack has under 3/4 of his max HP, the player should be prepared to heal directly after Minerva uses Krysta.
Minerva also uses a slow-moving but high-damaging homing attack called Crimson Flare. It is possible to avoid this attack by running, but if it hits it will do serious damage.
Equipping the SP Master is recommended, as it will reduce the damage and increase damage considerably (approximately doubles Zack's damage output and reduces damage taken to 0, if mastered) by spending Soldier Points. A good equipment setup is Ziedrich, Genji Armor, Genji Glove, and Genji Shield or Protect Ring and materia that boost Strength, Vitality, Spirit, and HP to the maximum. With the stats and equipment, if Zack guards, Minerva's attacks will cause between 100 and 7,000 damage. One should be sure to have at least 20 million SP.
To have a large amount of SP or money, one can mug 99 Phoenix Downs from Minerva and sell them, then buy a lot of Dualcast Materia and convert to SP. If playing on hard mode, an alternate and easier method is using Materia Fusion and the 99 Phoenix Downs to create a Curaga Materia with +999 HP stat (Curaga + Libra + Fat Chocobo Feather to convert the attached stat to HP and then Curaga + Libra + 99 Phoenix Downs to max out the HP stat) and then converting it to SP. This Curaga Materia takes approximately 1 million SP to make, but when converted, grants 2 million SP. The Dualcast Materia can be bought from the Net Shop Shade.
Gil Toss method
Gil Toss does over 99,999 damage, and is faster to execute than Costly Punch or Hammer Punch. The player can keep using it as fast as possible until Minerva dies as long as they have enough gil. The player can equip one Gil Toss materia and fill the rest of the slots with SP Master materia. It is not necessary for any of the materia to be mastered. Some of the information of the Costly Punch method of beating Minerva still applies here, like having an item equipped to break the damage limit.
The player should have at least 60 million gil. Gil Toss is a reward in Mission 4-4-4, and it can also be retrieved in a treasure chest in Missions 7-4-6, 8-6-3, and 9-5-3. It can also be stolen from Scissor Devil, a random enemy in Missions 9-5-2 and 9-5-3 and created via Materia Fusion by upgrading from Mug or Smart Consumer. The player can farm gil by stealing 99 Phoenix Downs from Minerva and selling them at any shop. (Another less efficient way of accumulating Gil is by getting the rare steal of Gold Rolling Pin x4 from the Holy Tonberry boss in Mission 9-6-2.)
The player should have at least 10 million SP for SP Master. SP Master materia can be stolen from Abyss Worms in Mission 9-6-4. The player can farm SP by buying Dualcast materia from the Network Shade Shop (found in a chest in Mission 4-6-2) and converting them to SP, or by using Materia Fusion and roughly 97 Phoenix Downs to create a Curaga Materia with +999 HP stat (Curaga + Libra + Fat Chocobo Feather, see below for details) and converting it to SP.
Recommended equipment is the Genji Helm (bought from the Network Shade Shop for 1,000,000 Gil) and the Genji Glove (found in a chest in Mission 9-6-4). The rest of the equipment is up to the player's preference, although most recommendations use the Ziedrich (halves all elemental attacks received, ATK +100, VIT+100, MAG+100, SPR+100, found in a chest at the end of a path in mission 9-5-6) and the Protect Ring (keeps Barrier and MBarrier active, bought from Mythril Mine Trading for 30,000 gil, or as a reward for completing Missions 7-6-2, 9-3-2 or 9-5-3), or using some other combination of equipment, but the Genji Glove and Genji Helm are standard.
Behind the scenes
The hardest group of missions becomes available early in the game, right after Zack is promoted to a SOLDIER 1st Class, thus it is possible to do these missions before receiving the Buster Sword, especially if the player is playing in New Game Plus. The Minerva battle starts off with a cutscene showing Zack with the Buster Sword even when it hasn't been obtained yet, and because the cutscene transfers directly into the battle, the Buster Sword remains on Zack for the battle. However, wielding different weapons is merely cosmetic in Crisis Core -Final Fantasy VII-, so it won't affect anything outside the sword's appearance.
The golden wheel with angel wings sprouting out on Minerva back's superficially resembles the dharmachakra, a widespread symbol in Buddhism, often used as a decoration in temples, statues and inscriptions, used to represent the Buddha's Dharma (Buddha's teaching and the universal moral order), Gautama Buddha himself, and the walking of the path to enlightenment. Gautama Buddha is said to have set the "wheel of dharma" in motion when he delivered his first sermon, and the turning of the wheel signifies change with universal consequences.