Lithos has 65,000 HP, 100 Defense, and 300 Magic Defense. She is weak to Fire and Pierce-type attacks, while being resistant to Light, Dark, and Slash attacks. Despite Lithos' low defense, she has absurd evasion (140) that would make dealing with her via melee attacks a chore. However, it's doable, and as a result, there are a few ways to go about this boss fight.
Of note is that she has some VERY annoying negative statuses at her disposal, so you should be prepared to be ready for Petrification and Charm, as well as an attack(?) debuff. Lithos, amusingly, can be poisoned.
Recommended team: Sakuya, Byakuren, Sanae, Marisa, Patchouli, Aya as commander.
Using this team lets you completely skip every single issue that this boss could possibly give you. It pretty much becomes a basic land-manipulation strategy, which is surprisingly effective and more than capable of taking down 65,000 HP. Sakuya will need 25 points in her Time Stop and Greatsword trees, Full Moon Revenge (フルムーンリベンジ), Private Square (プライベートスクウェア), atleast 12 bombs (I ran 15 just to be safe, this can be done by having 25 points in her Time Stop tree (she gets +2 at 20points in, but you'll be running 25 points anyways), 7 points in her Illusions tree (I ran 10 in this tree for the increased double attack chance) (also +1 Bomb), using her sixth-tier greatsword (also +1 bomb), her second character armor (+1 Bomb), and giving her the +5 Bomb accessory, for a grand total of 16 bombs), and as much MP as you can give her without compromising elsewhere.
Byakuren needs Elemental Weapon (エレメンタルウェポン) and Weapon Bless (ウエポンブレス). She'll be using Fire when she uses Elemental Weapon, and will be reinforcing attack buffs after the first Private Square.
Sanae needs Sword's Wind (剣の風) and Prayer's Wind (祈りの風). This is IT. It's up to you to decide what else your Sanae should bring.
Marisa needs Phoenix (火の鳥) and Extreme Heat (極限熱量). Like Sanae, it's up to you to decide what else to bring. Equip her with as much +Fire damage gear as possible, though. You'll want her spitting out as much damage as possible (unless your Patchouli has Sungrazer Comet; see below). 25 points in her Astronomy and Magic Mushroom trees.
Patchouli needs, if you have it, Sungrazer Comet (サングレーザーコメット, level 67), but if you find yourself without it, then Agni Radiance (アグニレイディアンス) paired with Fire Crest (ファイヤクレスト) will do just fine. Obviously, Hot Spot Vulcan (ホットスポットヴォルカーノ) and Active Elemental (アクティブエレメンタル) should be used to get the land-manipulation gauge to max Fire as soon as possible, but without compromising speed.
Aya will need 12 bombs. Therefore, 25 points in her Reporting tree, giving her her first character armor, and the +3 Bomb accessory will get you to 12 bombs.
Recommended formation is the one Orin gives you, as it boosts all fire parameters. If you do not have this formation, then any formation which raises physical attack will be fine.
On the first turn, you should use Aya's 3bomb commander move to set up a Private Square. Have Byakuren use a fire-property Elemental Weapon on Sakuya, Sanae uses Sword's Wind, and Marisa uses Phoenix while Patchouli uses either Hot Spot Vulcan or Active Elemental to raise the Fire land. Once the Private Square activates, proceed to mow Lithos down with Full Moon Revenges. Once the three turns inside Private Square are done, repeat the process, but this time have Byakuren use Weapon Bless on Sakuya to overwrite Sanae's attack buff, while Sanae uses Prayer's Wind to boost Marisa's and Patchouli's spell damage. Rinse and repeat until Lithos is dead, and hopefully she shouldn't even last long enough to get an attack off.
suggestion: all your characters should be level 80 minimum and should be full-geared. It will make the boss fight faster and easier. For even better results, level all your characters to 99 and get the best equipments but it will take a LONG time.
The difficulty spikes from here and you will fight the three gorgon sisters at once. In this fight, you are required to divide into 2 teams.
You want to use your best characters at the last part of the battle (preferably Youmu/Byakuren/Patchouli - you can use any 2 other characters to your preference) where you will fight the hardest boss of the game.
For the 1st part of the battle, the three gorgon sisters will each switch places every 3 turns. They will also summon two random monsters. You want to keep the 2 weakest monsters in the field so they don't get to summon the stronger ones.
You will need stone/paralyze/charm/poison resistance gears for this fight.
All 3 bosses share the HP meter. In total, they have 70000 HP. After you defeat them, they will run away but you will fight them again. However, it is not possible to defeat them this time (well you can but it's a waste of time doing this) so try to keep your characters alive for as long as possible. Watch out for the attack that deals 666 fixed damage (this deals 100 EXORCISM rate so divine protection cannot reduce this damage, can be reduced with mystic resistance?), it can stone any of your characters at a high rate (only blockable with +5 stone resistance, can pierce through +4 stone resistance). Also spells to watch out is Meteor which can deal a lot of damage to all your characters. At the beginning of the 2nd battle, you should switch party and start buffing up your second party to prepare for the last part of the battle.
(Note: This summary will be revised.)
After you deal enough damage and enough turns pass by, something happens.......
The three gorgon sisters begin to fuse themselves into one and there appears the 3 Gorgon Goddess! This is the hardest boss in the entire game.
This boss has 99999 HP and can attack 3 times per turn.
You should have Patchouli in the party. A properly geared and strengthened Patchouli can erase half of the land gauge when it is filled. If you do not have her in the party, you will likely lose the battle.
The boss will select one element at random and will cast magic of that element to fill the land gauge. It takes 1 cast for the gauge to fill it up completely so be careful. If one of the land gauges go to "active", on the next turn, the boss will absorb the element to heal 10000 HP and will cast Void Cavitation that will deal 777 fixed damage to all of your party. Void Cavitation damage can be reduced with a certain gear (mystic resistance?)
The boss cannot absorb Dark and is weak to this element. Youmu should be using the weapon that deals extra damage to "Foreign-God" type and receiving Dark element endowed by Byakuren as well as attack-up buff. NOTE: Magic will NOT work well as the boss has very high magic resistance, avoid using it unless you intend to flood the Dark element gauge. The boss has 33 divine protection which will reduce damage from all types of attack. Youmu is the only character capable of dealing high damage.
NOTE: The boss gains another form of divine effect which causes Youmu's highest tier techs to miss for any specific sword stance type. Requires a very high hit rate to hit. Criticals can MISS also so use only the 2nd-tier sword techs which should hit without missing. The 3-bomb sword techs can be usable as well.
Do not bother with stone resistance equipment due to the fact that the boss can use a full screen stone spell that ignores resistance! Automatic game over unless you have Alice to tank all the stone effect or get lucky somehow to avoid being stoned. (although the stone spellcard should be 100% hit)
You also need a healer that can heal all parties every turn because the boss is actively dealing damage to your party.
The boss will constantly dispel which could be a major nuisance especially to Youmu when she loses all her buffs! Requires high RES to dodge dispel. One dispel could potentially be fatal!
Good luck! You need lots of it!