Blue Dragon

For this achievement you must defeat all 5 Dragons scattered around the world map, after defeating all 5 you will receive the achievement, this is also necessary to obtain the Dragon Bracelet achievement.

1. Moody Dragon: Found in the Underground River, where you will see a TON of Kelolons, you must defeat ALL of them, once you do that the Dragon will appear.

Battle: Very easy fight simply just lay into him with high powered physical attacks and he should go down without a hitch.

Note: If you haven't done so already you will need to visit Kelaso Village and complete the side quest there before the Spark Dragon will appear.

(Sidequest)

2. Spark Dragon: Found in the Gul Mountains, take these directions from the Warp Device: left, right, right, left, left.

Battle: Obviously weak to water, keep up the high level water spells and Corporeal attacks to take him down. His attack is pretty high so make sure you are well healed as well.

3. Phantom Dragon: Found in the Great Desert on the southern-most point. Warp to Lal Mountain Camp then fly there.

Note: If you are going for the Complete Item Record, you MUST steal Nene's Earing from him, you only get one chance to steal at the very beginning of the fight and if you don't get it then reload your save and fight him again until you steal it on the first try.

Battle: This dragon is ONLY weak to Wind attacks anything else won't work or will heal him. Use Windus or Windus sword to take him down and stay fully healed. Also do not use Corporeal attack as they will heal him as well.

4. Blizzard Dragon : On a small hill west of Kelaso Village.

Battle: Attack him with Flarus and Flarus Sword only and keep your allies healed.

5. Amethyst Dragon: Exit Jibral and head South-West, follow the road to the coast, then follow the Coastal Road around to the dead end and the Dragon will appear.

Battle: Not necessarily weak to anything, just keep up the physical attack. Magic Sword works great as well as Charge Attack. Corporeal attacks also work great here as well.

Being between Level 70-80 is more than enough to take these guys down without much of a problem, anything lower (besides the Moody Dragon) will prove to be a tough battle.

I read online a really easy strategy for beating the dragons. I have tested it and it works really well on the Amythest and the Phantom Dragons. Sadly it does not work on the Blizzard or Spark Dragon. Moody Dragon is a pretty easy fight regardless so this was not necessary.

A level 30 the Monk learns a skill called Total Guard. This skill allows the Monk to take the hit for every party member.

There are 4 accessories: Bellybutton Ring of Wind, Fire, Water, Earth.
What those do us allow the wearer to get healed from elemental magic.

Locations:
Bellybutton Ring of Water: Lot Wilderness West, Green barrier
Bellybutton Ring of Fire: Ancient Ruins Cavern, Red Barrier
Bellybutton Ring of Wind: Underground Cavern
Bellybutton Ring of Water: Alumaru Village, Treasure Storehouse

The Amythest Dragon does a lightning attack that is considered wind.

I had my Monk in the front row with Total Guard and the Bellybutton Ring of Wind. I had my other 4 party members in the back as Black Mages.

All the Amythest Dragon would do is it's "Lightning of the Gods" attack that was a single target attack. My Monk would jump in the way and get healed from it. My other characters used Flarus from the back and destroyed him.

The same thing worked for the Phantom Dragon. He does a wind attack and Total Guard would jump in front of it and heal. The Phantom Dragon would do an AoE wind attack that would cause me to have to heal, but with wind resistance on all my party members it was not enough damage that I couldn't easily heal from.