Preparing for Battle
If you have visited Kelaso village up near the northernmost part of the Blue Dragon world, you have found the strange hat-wearing people there and heard their stories. One such story, by the elder named Bauhm, tells of five dragons that possess incredible power. If you defeat these dragons, you learn, you will obtain this power. These dragons are no easy task. It is easily possible to beat the game, including the final boss, and still be too weak to kill the dragons, especially the harder ones. In order to prepare for the battle, you should level at least one class up to 75 with each character, and have them use that class in the battles. The more classes and skills you have unlocked, the better, but you will need the sheer power of one higher level class in order to emerge victorious
Another recommended way to prepare is obtaining all the Bellybutton Rings before fighting the dragons. These rings will grant the wearer the ability to absorb their element, making that person almost impossible for the dragon to kill. I would recommend equipping your healer with the appropriate ring for each battle, as that will allow them to keep the rest of the party alive as long as needed.
The Moody Dragon
If you travel to the Underground River, you will have found a seemingly-pointless dead end that is filled with Kelolons all over. Defeat all of them, and then try to leave the room, and the Moody Dragon will appear. This is by far the easiest of the dragons, and can be defeated with standard boss tactics, using one or two characters for heals, and the rest for spamming attacks. If you want, you can steal a Lei from this dragon, a very useful item that guards against status effects. After this dragon, you must make sure you have spoken to Elder Bauhm, or the rest of the dragons will not appear.
The Phantom Dragon
Travel to the Great Desert, where the crystal spikes emerged from the ground, and go to the southernmost point. There you will face the Phantom Dragon, which uses the power of wind, so equip your Bellybutton Ring of Wind. There is one very challenging part about this boss - it cannot be hurt by physical attacks, so avoid them at all costs, and prepare accordingly. If you do strike it, it will heal itself, which on top of the lower damage your melee attackers will do, makes this the most drawn out of any of the dragon battles, so be ready for a long fight. Also, the physical attack restriction applies to Corporeal attacks, so unless you are a glutton for punishment, avoid using them as well.
The Spark Dragon
When you visited the Gul Mountains earlier in the game, you may have seen a room blocked off by a red barrier. This room contains the Spark Dragon, and you will fight it immediately upon passing the barrier. This is a pretty straightforward fight, but equip your Bellybutton rings of Earth and Wind beforehand to make it even easier. The only really unique thing about this boss is its speed, but if your characters are sufficiently powerful, you should not have too much difficulty taking it down.
The Amythest Dragon
Returning to the Coastal Road near Jibral, you can go along the path that was previously blocked off by a large rock. Near the rock, you find the Amythest Dragon, which has quite a bit of HP. Thankfully, its attacks are not very powerful, so just equip your Bellybutton Ring of Wind before the right, and go in with guns blazing. This particularly fight should be primarily offensive for you, with healing more of a secondary priority. If you pummel the dragon for enough time, it will fall, and you will emerge victorious over your fourth dragon.
The Blizzard Dragon
This is the most difficult of the dragons you will face, and is found just outside of Kelaso Village, on a small snowbank. Like the name implies, it is an ice dragon, so equip your Bellybutton Ring of Water to be safe. This dragon has very damaging attacks, and also has the ability to freeze your characters, which can turn the tide of battle quickly. I would recommend two healers for this battle, keeping your two attackers alive as much as possible. Spam the dragon with Corporeal attacks and Flarus and it will eventually fall.
Reaping your Rewards
After defeating all of the dragons, return to Elder Bauhm in Kelaso Village, and present him with the five dragon fangs. You will obtain one of the most powerful items in the game, the Dragon Bracelet, and unlock an achievement for doing so, as well. If you have difficulty with any one particular dragon, focus on their weakness, and make sure your characters stay alive! That is the most difficult part of the dragon fights. Good luck, and good dragon hunting.