This FAQ will only cover bosses after escaping from the Ship Graveyard. For all the bosses before Carwen, just keep attacking and heal with potions/white magic when necesary.
Before going into North Mountain, train with 3 Knights and 1 White Mage until the White Mage gets White Lv1. When that happens change the White Mage into a Knight and train the 4 Knights until they all get Two-Handed. This will help A LOT. Have 3 Knights with Two-Handed ability and 1 Freelancer with White Lv1 and Two-Handed abilities. Buy the best weapons in Carwen. Proceed through the story.
~MAGISSA~
She'll die in 4-6 attacks with the Two-Handed ability.
When you obtain Hiryu, go to Tycoon castle, sleep the night and find the treasure, that includes the Ashura katana. With Two-Handed, a high enough level and a critical hit (Trust me, you'll get lots of them) you will hit ~1000 damage! So early in the game! So make another freelancer (don't equip it on the freelancer that has White Lv1) and equip Two-Handed, another ability of your choice and the Ashura. Proceed through the story.
~GARULA~
Keep attacking it. A critical hit from the Ashura and 2-3 more hits will kill it. Just keep attacking it.
Proceed to Karnak. Before going to the Fire-Powered Ship, buy a total of 2 Frost Rods - also buy another Rod of your choice and the best weapons available. If you want to go get Shiva, buy 2 Flame Rods as well.
Important note : To Use a Rod, equip it on someone, go to the item menu in battle, go all the way up until you can select your weapon and your shield, and "use" the Rod you have equipped like you would use a normal item. It will cast a tier 3 (-aga) elemental black magic spell on your enemies, dealing a lot of damage. The element depends on your rod. (Flame Rod = Firaga, Frost Rod = Blizzaga etc.)
~SHIVA~
Use 2 Flame Rods. Dead.
~LIQUID FLAME~
Use 2 Frost Rods. Dead.
Important note : Iron Claw carries the powerful Death Claw blue magic spell. If you want it, have at least 1 Blue Mage, kill the wolves, wait until he transforms and then wait until he casts Death Claw on your Blue Mage(s). After you do that, proceed with the strategy.
~IRON CLAW~
Use the extra Rod I told you to buy earlier. Dead.
Buy 2 more Frost Rods and 2 more Flame Rods. Proceed to the Library of the Ancients.
Important note : Get the Level 5 Death blue magic from the Page 64 enemy. To get it, your blue mage's level needs to be divisible by 5 (5, 10, 15 etc.). If he isn't, level him (stay away from the desert! Dhorme Chimeras are powerful!) until he is. WATCH OUT! If your whole party's level is divisible by 5 and P. 64 casts L5D, it's game over. So anyway, get L5D.
~IFRIT~
Use 2 Frost Rods. Dead. (battles are getting harder and harder, eh?
)
~BYBLOS~
Use 2 Fire Rods. Dead. (there is a little chance that he might survive - if he does, keep attacking it until it dies)
Get the black chocobo. Go to Lix Village and buy as many Lightning Scrolls (or any other scroll) you can. Land in the forest just below Crescent Island. Have 1 Ninja, 1 Beastmaster, 1 Blue Mage and 1 White Mage (the white mage you used earlier as a freelancer). Walk on the land (not the forest!) until you encounter 5 Black Flames. Throw a Scroll at them - they all die, giving you great ABP and EXP! As long as you don't walk on the forest, you will ALWAYS encounter 5 x Black Flame. Grind on them until you get Control, Blue and White Lv3. Revert back to your old party. Proceed through the story.
~SAND WORM~
There isn't any way to beat this boss very fast. Keep attacking or just use some rods. Your call.
~ADAMANTOISE~
This is just one of the reasons I told you to get Level 5 Death. Since his level is 20, L5D will kill it instantly.
Get 2 or 3 Lightning Rods.
To kill the lesser cannons, either use Death Claw + attack on them or have 4 Geomancers and spam Geomancy.
~SOUL CANNON~
Start the battle with Level 5 Death, then use 2 Lightning Rods. If it doesn't die, use another one or just attack it normally.
Control a Lamia in the Ronkan Ruins and have her cast 1000 Needles on your Blue mage. When you get close to the Archaeoaevis have 4 Blue Mages ready.
~ARCHAEOAEVIS~
Spam 1000 Needles until it revives itself. Then cast Level 5 Death. Awesomesauce.
~TO BE CONTINUED!~
Before going into North Mountain, train with 3 Knights and 1 White Mage until the White Mage gets White Lv1. When that happens change the White Mage into a Knight and train the 4 Knights until they all get Two-Handed. This will help A LOT. Have 3 Knights with Two-Handed ability and 1 Freelancer with White Lv1 and Two-Handed abilities. Buy the best weapons in Carwen. Proceed through the story.
~MAGISSA~
She'll die in 4-6 attacks with the Two-Handed ability.
When you obtain Hiryu, go to Tycoon castle, sleep the night and find the treasure, that includes the Ashura katana. With Two-Handed, a high enough level and a critical hit (Trust me, you'll get lots of them) you will hit ~1000 damage! So early in the game! So make another freelancer (don't equip it on the freelancer that has White Lv1) and equip Two-Handed, another ability of your choice and the Ashura. Proceed through the story.
~GARULA~
Keep attacking it. A critical hit from the Ashura and 2-3 more hits will kill it. Just keep attacking it.
Proceed to Karnak. Before going to the Fire-Powered Ship, buy a total of 2 Frost Rods - also buy another Rod of your choice and the best weapons available. If you want to go get Shiva, buy 2 Flame Rods as well.
Important note : To Use a Rod, equip it on someone, go to the item menu in battle, go all the way up until you can select your weapon and your shield, and "use" the Rod you have equipped like you would use a normal item. It will cast a tier 3 (-aga) elemental black magic spell on your enemies, dealing a lot of damage. The element depends on your rod. (Flame Rod = Firaga, Frost Rod = Blizzaga etc.)
~SHIVA~
Use 2 Flame Rods. Dead.
~LIQUID FLAME~
Use 2 Frost Rods. Dead.
Important note : Iron Claw carries the powerful Death Claw blue magic spell. If you want it, have at least 1 Blue Mage, kill the wolves, wait until he transforms and then wait until he casts Death Claw on your Blue Mage(s). After you do that, proceed with the strategy.
~IRON CLAW~
Use the extra Rod I told you to buy earlier. Dead.
Buy 2 more Frost Rods and 2 more Flame Rods. Proceed to the Library of the Ancients.
Important note : Get the Level 5 Death blue magic from the Page 64 enemy. To get it, your blue mage's level needs to be divisible by 5 (5, 10, 15 etc.). If he isn't, level him (stay away from the desert! Dhorme Chimeras are powerful!) until he is. WATCH OUT! If your whole party's level is divisible by 5 and P. 64 casts L5D, it's game over. So anyway, get L5D.
~IFRIT~
Use 2 Frost Rods. Dead. (battles are getting harder and harder, eh?

~BYBLOS~
Use 2 Fire Rods. Dead. (there is a little chance that he might survive - if he does, keep attacking it until it dies)
Get the black chocobo. Go to Lix Village and buy as many Lightning Scrolls (or any other scroll) you can. Land in the forest just below Crescent Island. Have 1 Ninja, 1 Beastmaster, 1 Blue Mage and 1 White Mage (the white mage you used earlier as a freelancer). Walk on the land (not the forest!) until you encounter 5 Black Flames. Throw a Scroll at them - they all die, giving you great ABP and EXP! As long as you don't walk on the forest, you will ALWAYS encounter 5 x Black Flame. Grind on them until you get Control, Blue and White Lv3. Revert back to your old party. Proceed through the story.
~SAND WORM~
There isn't any way to beat this boss very fast. Keep attacking or just use some rods. Your call.
~ADAMANTOISE~
This is just one of the reasons I told you to get Level 5 Death. Since his level is 20, L5D will kill it instantly.
Get 2 or 3 Lightning Rods.
To kill the lesser cannons, either use Death Claw + attack on them or have 4 Geomancers and spam Geomancy.
~SOUL CANNON~
Start the battle with Level 5 Death, then use 2 Lightning Rods. If it doesn't die, use another one or just attack it normally.
Control a Lamia in the Ronkan Ruins and have her cast 1000 Needles on your Blue mage. When you get close to the Archaeoaevis have 4 Blue Mages ready.
~ARCHAEOAEVIS~
Spam 1000 Needles until it revives itself. Then cast Level 5 Death. Awesomesauce.
~TO BE CONTINUED!~