Obviously from the description, the way I play completely disregards Anna (minus one extremely specfic case).

This is a basic how-to guide.

NOTE: ALL BOSSES ARE CONSIDERED TO HAVE EPIC-MODE STATS (200% higher than normal). I HAVE PLAYED THROUGH THE STORY THREE TIMES AND BEATEN ALL THE BOSSES (Battle Mountain and normal), THE RUSHES, AND HAVE GOTTEN TO WAVE 30 ON ENDLESS BATTLES (all in EPIC mode). I think I know what I'm talking about. I am also looking at the game as I write this to double-check names and info.

So let's refresh the bosses in question (which is all of them. I might add pictures later):
Mighty Oak and Armored Oak
Crystal and Diamond Golem
Praetorian MKI and MKII
Rafflesia and Rainbow Rafflesia
Zombie Hydra (Not technically a boss, but still extremely tough considering you only get the winged boots right before the screen with Godcat)
Godcat
The Creator and Destroyer (This is different from Godcat)
The Dark Players (Evil versions of Anna, Natz, Matt, and Lance)
The Glitch

The guide will take this into consideration when fighting the bosses:
-All gear acquired (Flair, Armor, and Weapons)
-Level 5 (3 for flair) Equipment. You'll at least have the important gear by the Godcat battle in the first run.
-Level 49 characters (For the 3rd run only. I'm not entirely sure what level I beat Godcat at in the previous runs)
-You've literally ransacked the Rare Item shop. Most expensive item is 32 MILLION gold. Or 512K at the end of the 1st run.
-Important skills maxed out. Includes Limit Breaks (1st run)
-Most skills maxed out. Includes Limit breaks. (2nd run)
-All skills acquired and maxed out. Includes Limit Breaks. (3rd run)
-All summons acquired (meaning you've beaten the Glitch)

The summons. What's effective against who and who exactly should use what summon.

Alright. A quick refresh of the summons:
-Scanbot, Friend Dog, NoLegs, Sludge Slime, Coal Bat, Narwhal, Mad Cactus, Frost Sprite, Ancient Monolith, Slime Bunny, Giant Squid, Thunder Elemental, Wooly Mammoth, Beholder, Chimera Bear, Kitten Fort, Evil Worm, Frost Wraith, Red Dragon, Gem Idol, Praetorian, Protector, Cosmic Monolith.

Here's the REALLY useful ones for these characters:
-Scanbot (Until the Bestiary is filled)
-Friend Dog (Use only in a pinch though or with the Puppy hat)
-Gold Dragon (Useful against Dark foes, and will give the party HP, usually full HP)
-Praetorian (Attack buff [70%] and Brave for 4* turns)
-Protector (Useful to Dispel, and deal major Bomb damage to everyfoe)
-Cosmic Monolith (The game tells you it's the most powerful summon. Only thing is it's a dark summon, meaning it's only effective against foes weak to dark.)

Summons effective with these characters:
1) Anyone (Support, no damage)
-Scanbot, Friend Dog
2) Matt (Physical Damage)
-Praetorian
3) Lance & Natz (Magic Damage)
-Gold Dragon, Protector, Cosmic Monolith

Summons effective against these bosses:
1) Gold Dragon
-The Destroyer, all the Dark Players, Zombie Hydra
2) Praetorian
-Any as it's non-elemental, but the lower the defence, the better.
3) Protector
-The Creator, Dark Lance, Crystal and Diamond Golem, Praetorian MKI
4) Cosmic Monolith
-The Creator (moreso than the Protector), Armored Oak, Diamond Golem

Other info:
-Given that Natz will have higher Magic Att., have her use the useful summons instead of Lance. Although Lance has lower mag. att., he still will do decent damage against foes with a weakness to the summon's element.
-Continuing with the previous, Lance will more than likely be using the summons more often than not given that Lance dies constantly in this kind of playthrough, and Natz will need to revive him.
-Even though the Praetorian gives a buff to all the players, and using Matt to summon uses his turn, it's still effective against a boss like Dark Matt who deals an insane amount of crits.
-Do use the other summons if a situation calls for it. Since Matt doesn't have any real Wind skills, Gem Idol will be GREAT for dealing phy. damage to all foes weak to wind. Kitten Fort is amazing (after meeting the prerequisites of the morale effect) in the Glitch battle.

Being the person I am, I focus mainly on doing CONSISTANT damage throughout the battle. Meaning Matt and Natz can effectively do over 1M damage per hit (for single-hit skills like Judgement and Cataclysm) against any given enemy.

DISCLAIMER: THIS GUIDE DOES NOT SHOW HOW TO GET 3- OR 30M DAMAGE.

Obviously, Anna will get NO food.

General rules for food:
-All Ham goes to Matt. No questions asked.
-All cake goes to Natz. Though if you'd like, Lance can get some in the 2nd and 3rd playthrough.
-Generally, split the lollipops equally throughout the 3 characters. As long as everyone's (including Lance's) acc. is above a normal foe's evade you'll be fine.
-Most of the candy canes go to Matt. You really want him to live. And in Epic mode, evade might be the best defence he gets.
-Honeycombs go to Matt only 1st playthrough. Same with Sushi to Natz. 2nd and 3rd do however you'd like.
-Donuts and Steak will go only to Natz and Matt (respectively) in the first playthrough. Start to switch it in the 2nd and completely do so in the 3rd.

Other info:
-Seriously, make sure Matt gets all the Ham and Natz the cake. Matt'll end up with about 8000 attack, Natz's will be higher than 7100 if you don't accidently give food to the wrong person.

This'll only cover what equipment stays constant throughout a playthrough.

For Matt:
Equililbrium, Casual Cap, Gold Armor, Green Cross.

For Natz:
Pope's Dress, Angel Pin

For Lance:
Cursed Charm


Why?

Equilibrium gives Auto-Revive randomly to Matt. Gives a +100 boost to attack AND mag. attack. Can SYPHON foes. And counter attacks with LEGEND.
Casual Cap displaces the acc. and evade reduction from Equilibrium, and gives Syphon, Stun, and Doom/Death resistance.
Gold Armor gives 100% resistance to Fire, Ice, and Lightning. Gives a decent boost (+50 def, +30 mag. def.) to defence, and buffs defence when hit with a strong attack.
Green Cross is to keep him alive for longer. He's the only one able to stand against Godcat in the third playthrough BY HIMSELF and beat her.

The Pope's Dress casts Revive on a random LIVING player at the beginning of the turn. Plus gives Curse resistance.
Angel's Pin gives the wearer Auto-Revive. Just makes sure Natz can get Auto-Revive more often.

Cursed Charm gives 30% dark resistance, plus has the chance to Curse foes. So if you have trouble getting a boss' defence down, use Hyper Beam, curse them, and wait a bit.

These are for the Special skills and Limit Breaks only. Obviously.

This is the list I have for my team:

Matt:
-Purify, Protect, Guardian, Spark, Big Spark, Plasma Cage (should change that), Icicles, Blizzard, Giga Drill, Acid, Geyser, Flood, Holy Fire, Dark Flare, Tsunami, Death Metal, and Power Blast.

Natz:
-Heal, Healmore, Revive, Beserk, Hellfire, Hailstorm, Toxic, Blast, Big Blast, Airwave, Shockwave, Bubbles, Bubble Blast, Talisman Seal, Absolute Zero, Supernova.

Lance:
-Cleanse, Lock On, Barrier, Solar Flare, Bind, Debilitate, Syphon, Dispel, Sawblade, Triple Sawblades, Fire Spin, Ion Cannon, Black Hole, Rapture.

Some changing around will be needed, but otherwise, this is my list.

Matt generally deals all the physical damage, and gives the attack, defence, and evade buffs.

Natz heals and revives, deals major magical damage, and gives the mag. attack buff and can berserk foes.

Lance buffs and debuffs, cleans status effects and debuffs, and does some magical damage.

So how do you use the above stuff to your advantage?

Simple. You do.

♥♥♥♥♥♥♥-ry aside, here's how:

1) As a general rule, use Temper first turn on Matt.
2) Try to charge Hyper Beam with Lance.
3) DOUBLE-CHECK EVERYONE'S EQUIPMENT. Elemental and status effect resistance is needed, especially against Godcat and the Foe and Mini-boss Rushes.
4) If you can, cast charm on Natz. The buffs will help.
5) In case of a breather wave (or the first, third, and fifth waves against Godcat) use Guardian on Matt and Natz.
6) Cast Barrier from Lance.
7) Dispel when needed. Meaning you dispel when all the foes have buffs, or when the boss has one. Or both.
8) Keep these debuffs and status effects off at all times: Attack (Matt and Lance), Mag. Attack (Natz), Defence and Mag. Defence (Everyone), HP (Everyone, especially Matt), Accuracy (Everyone), Doom, Freeze, Stun, Syphon, Curse, Weakness, Dispel.
9) Keep Auto-Revive on Matt and Natz. Especially if they buffs on.
10) Try to get at least 50% resistance against a boss' element. 100% is better, higher is perfect. This'll happen in the Godcat fight with the right equipment.
11) Lock On is good for bosses like the Glitch and Praetorian MKII, who's evade is abnormally high. Put it on Matt at first, then Natz, and finally Lance.
12) Use some damn common sense. If a boss is weak to Fire, equip fire-element weapons (DO NOT SWITCH MATT'S WEAPON) and use fire-element skills (Eruption, Hellfire, Bullet Hell, etc.) and summons (Red Dragon, Sludge Slime)
13) Do not switch any of the "Constant" gear unless absolutely necessary.

*IMPORTANT*
14) Given that you don't have Lance until AFTER you beat Mighty Oak in the first playthrough, make sure that Anna is as optimized as possible before the battle. Equipment as high level as possible, skills able to beat down the boss, etc.
15) If all three characters get KO'd, meaning Anna is sent out onto the battlefield, MAKE SURE SHE IS PREPARED TO FIGHT. Do give her the correct equipment to protect herself against foes, as well as the needed buffs and everything to make sure she, and the others, get out alive.
*IMPORTANT*

16) Try your hardest to keep EVERY character alive (including Anna) at the end of every battle. It's always a good idea to keep even a character you don't use at equal level so that they can stand their own.
17) After you get Lance, focus on only maxing out Matt, Natz, and Lance's stuff. Leftovers should be used to craft Anna's stuff.
18) Never leave a chest unopened.

A few things.

1) This is all based off my three playthroughs of the Steam verison of the game.
2) All this is also based on how I play. If you play it differently, don't try to change this to how you play.
3) I've never seen a guide for just three players. Thought I'd make one. Though I'd appreciate links if there are any others.
4) If I were to use all 4 characters, I feel I'd be spreading out my food too much, and would possibly not have enough max-level equipment for the 1st Godcat fight. Because that fight was HARD.
5) If anyone feels I missed something that should be covered, SAY SO! I'm always open to that kind of stuff, and the same goes for if I have some details wrong.

Thanks for reading! This took quite a long time to make considering I lost an initial version because of an issue with Steam not letting me leave a section. Obviously, it's fixed.

Again, if there's anything you feel I missed or got wrong, say so!