Here's how I did all the optional bosses for anyone having problems. Anyone else who's already smacked them down please post your tactics/tips etc.
Sacred Beast - Numara Atoll
Once you get Ming and her harp to Numara Atoll you can summon this beasty for a battle. This is an optional boss that you don't actually kill, you just have to knock it back into its senses.
The first thing to know about this guy is that he has a doom spell which is unavoidable and can wipe out your entire party in one hit. It's very easy to spot it coming. What he does is cast a sleep spell on your entire party when his health drops below half. Once he does that you have 4 turns to finish him off or he breaks out the unblockable doom spell and your game is over. So obviously any items that prevent sleep would be very helpful. In addition to the anti-sleep item you will probably want to get anti-element stuff equipped also, as he breaks out all sorts out of element-based attacks. You can get an immunity to all elements item from the Kelolon village which is pretty helpful. Other than that, he's not such a tough guy. Physical attacks and element/curse spells will do a lot of damage to him.
Once you beat the Sacred Beast you get an item which gives your immortals +10 slots.
King Kelolon - Kelolon Village
This boss is the other one you don't actually kill, and the only thing that might bother some people is he is constantly aided during the battle, giving him healing and damage absorbing spells in addition to his own attacks. He isn't particularly tough to beat, but if you can't keep up a good rate of damage on him the helpers will heal him faster than you can knock him down. He also has the Divide spell (which you will learn upon beating him) that can do decent damage. Other than that he is a piece of cake.
Blue Dragon - Northern Snowfields
The Blue Dragon has the ability to absorb any element-based magical attack, so be careful you don't heal him during the battle. He also comes at you with a few high power black and curse magic spells. Equipping an anti-curse item and use of barriers is recommended for lower level players. Physical attacks with magical support worked best for me, and this boss shouldn't give you too many hassles as long as you don't let him use "Death" on your whole party.
The Yellow Knight - Uhra Castle
Simple. Just follow the instructions he gives you. If he wants you to attack, attack, if he wants you to defend, defend. The battle is a mere formality but if you don't do as he says he will kill you.
Cave Worm - Forgotten Cave
Going into the forgotten cave and entering the upper plateau area will trigger this boss fight. The worm isn't all that tough but it has just about every status effect spell in its arsenal so it can paralyze, blind, sleep, freeze, and also poison you, so equip your anti-effect items. After that it shouldn't present much of a problem.
The Legendary Curse Sorceror - Temple of Enlightenment
Mack has to be in this fight so don't neglect to level him up. This guy is a master of curse magic and always attacks twice in a row when his turn comes, so he can do some damage. He also conjures various beasties to protect him which you will have to defeat before you can take him down. The first protector he summons can be defeated with physical attacks and wind spells which seem to work well on all these critters. Once that is dead he will summon a pair of guardians which are very susceptible to "Death" so if you have it, use it! You can knock these 2 clowns out before they even know what hit them. Once they are down you get the main man himself, and he is also very weak against wind spells and physical punishment. Items which increase defence and anti-status effects will help a lot against this boss.
Persona - Old Sorceress' Mansion
If you go back to the room where you fought the mansion boss you will encounter Persona. This boss isn't especially tough but there are a few things to be aware of. First of all he uses mainly black and curse magic, watch out for "Death". Second he can become immune to either magic or physical attacks by turning his head. He can also do this quite quickly meaning you can order say Ming to cast a spell while he is showing his physical face but by the time she has it ready to fire he has already turned his head around, making your attack useless. I found the easiest way to beat this guy was to just throw bombs at him. If you don't like the idea of playing chance with his head-turning patterns you can always resort to bombs, as he cannot block these attacks. Just keep lobbing them at him and he will die pretty quickly. If you want to spice it up with some physical or magical attacks in-between, go for it, just keep an eye on the head rotations.
If tactics just aren't working and you are the type of guy that has problems ordering at McDonald's, you can of course just level grind until you can swat these guys like flies, but once you're finished with them, The Immortal is waiting for you in the Backyard
He is the ultimate answer to the problem of level-grinding brutes, and if you don't use tactics there you will be dead in a matter of rounds.
I’ve experiments to run.
There is research to be done.
On the people who are still alive.