Tantarian
During the rescue of Dagger in Alexandria, you have the option of fighting Tantarian. In general stand points, this is not a hard boss to fight. But it is a little difficult this early in the game. You might want to wait until Disk 3, when Alexandria falls under attack. Whenever you decide, you will find him in the west Library, at the last bookshelf. Simply talk to him, until the fight begins.
Preperations
Make sure to equip everyone who can have it with Devil Killer, and Antibody. If you have Auto-Regen, equip that as well. You will have no White Magic in either place, so it is a good thing to keep your HP up.
Make sure Freya can use Reis's Wind for an additional boost in HP recovery. If you have Amarant, try to get his Spare Change ability. And have Zidane with his Thievery Skill. That is, if you have been stealing enough.
When you feel you are ready, initiate the fight.

Boss fight: Tantarian HP: 21,997 Weakness: Holy

At first, Tantarian shows only as a closed book. You have to deal at least 180 Pt's damage, before it reveals its true form. This can be easily done with Zidane's Thievery, if you have been stealing enough. If not, try using Spare change, or simply attack, until the book opens to your foe. Once this does, stop all physical attacks. This will cause the book to close again. Hit is hard with any skills you have. Spare Change, and Thievery work wonders, as well as Freya's Cherry Blossom. If you do not have these, simply have Vivi cast his strongest magic, and everyone else support him. Eventually the book will close again, and you will have to go through the process again. The two major attacks in Tantarian's arsenal are Paper Storm, and Edge. Both of which are devastating, even on Disk 3. There is no real defense against these attacks, so be prepared to get a Hi-Potion or Elixir ready. While open, it will try to cast Venom on you. This is of course rendered useless by the Antibody ability. His other attack is Doom, which will give a 10 second count to death if it connects. When he opens up, have Vivi cast his strongest spell, and Amarant and Zidane use their skills. If Freya has no skills to use, simply have her jump. Striking Tantarian will cause it to close again, but the damage is worth it. Just keep plowing away, and he will fall pretty quickly. For defeating him, you get a pair of Running Shoes.

Hades
In Memoria, after a save, you will come to a room, where Quina will swim after the fish. Once she is finished, search behind the ledge, and you will get a message asking you to leave at once, or die. Speak again, and you will be taken into a fight with the lord of the underworld himself. This is a pretty challenging fight in lower levels. So let's take a moment to get ourselves prepared.

Boss fight: Hades HP: 55,535 Weakness: Holy

You would think Hades would be more of a threat, given he IS the loard of the underworld. But in fact, the fight I did was at level 35 or less, and I still came out a winner. But it was not so easy as it would be at a higher level. First he will cast Reflect on himself. This makes it extremely difficult to get any magic attacks in. If you wish to use magic, cast Reflect on a party member. Then you can bounce Flare off to Hades. Also his Judgement Sword should be something to watch out for. It will knock a character down to single digets real fast. Have the next person able heal them to a fighting chance, until Dagger can properly restore HP. When he begins a countdown, he will be powering up for either his Curse attack, or Doomsday spell. Both can be very devastating to you, if you did not prepare accordingly. It will also heal the boss, since it is shadow magic. His Cleave attack is similar to the Iron Giants attack, in it leaves a character with a single HP. Be sure to restore their HP as soon as you can do so. Hades usually goes after them in the nxt turn. If you do not attend to them fast enough, you may lose another turn bringing them back to life. His other attacks include mustard Bomb, and Freeze, but these are easily dodged with the Body Temp ability. The best attack is Steiner's Shock, which deals out 9999 damage each time. If Zidane Trances, his Grand Lethal will do the same. Flare will cause about 5-6000 damage, but you will have to sacrafice healing someone to reflect it off them. I used Vivi as a medic to revive members, and give Steiner and Dagger Ethers as needed. If you find yourself in great standings, have Dagger summon a boosted Bahamut for an additional 5000+ damage. Also, if you get the chance to, steal from him. He is carrying a good deal of things, including a Robe of Lords and Reflect Ring. Once you get him out of the way, you will get a Wing Edge or Elixir. But that is just the half of it.

Once the mighty Hades has been defeated, he will ask you to bring him two Pumice Pieces, and he will synthesis them for you. You actually do not need to do that, just speak to him again, and his shop is open for business. He can get you the most powerful items in the game, so take full advantage of his skills.

Item	Gil	Items needed
Robe of Lords	30000	White Robe, Black Robe
Tin Armor	50000	Hammer, Ore
Protect Ring	40000	Dark Matter, Rebirth Ring
Pumice	50000	Pumice Piece, Pumice Piece
Garnet	350	Ore, Remedy
Amethyst	200	Ore, Annoyntment
Peridot	100	Ore, Soft
Sapphire	200	Ore, Antidote
Opal	100	Ore, Potion
Topaz	100	Ore, Eye Drops
Lapis Lazuli	400	Ore, Dead Pepper
Pumice Piece	25000	Hammer, Pumice
Save the Queen	50000	Javelin, Silver Gloves
Phoenix Pinion	300	Phoenix Down, Gysahl Greens
Ether	500	Echo Screen, Vaccine