Blue Dragon

This is earned at the end of disc 2, in Nene's Fortress. You have one hour to get through this five-floor dungeon.

The achievement itself is obvious, so the point of this guide is to help you get through it without missing any of the unique monsters.

Keep in mind that the clock stops while you are in battle, but you are penalized by 30 seconds for each encounter, regardless of how many monster parties are involved. So use your Encounter ring and link multiple mobs to save time.

Here is a list of all monsters in the approximate order you can find them. None of the mobs is especially easy to miss, but it's nice to have a checklist. The only one to watch out for is Intercept Dynadrones. This is summoned by Versatile Mecha Robo, so let him take turns until he summons them.
Floor 1:
01. Steel-Crusher Leopard
02. Glowering Imp Trap
03. Stone Giant
Floor 2:
04. Ninja Ghost
05. Imposter Eye
06. Wandering Prophet
07. Horned-Viper Trident
Floor 3:
08. Red-Mask Robot
09. Balloon Bomber
10. Patchwork Puppet
Floor 4:
11. Versatile Mecha Robo
12. Intercept Dynadrones (Summoned by VMR)
Floor 5:
13. Enforcer Robot
14. Standard Defender
15. Assassin Robot

16. Servant Mecha Robo A
17. Servant Mecha Robo B

These last two occur with the boss. I'm not sure if you have to specifically kill them or not, but do so to be safe (I mention this because it's a scripted fight in which you're not supposed to attack the boss).

None of the treasure chests in here contains anything missable. I would not recommend going out of your way to find any of the chests, but by all means, if you have time. The final floor chests are right there behind the mobs you need to fight, so of course grab those. Besides the spells it's all worthless crap like Phoenix Talons, no accessories.

In case you care, the spells in here are:
Lv 5 - Regenera (Floor 2)
Lv 6 - Resistus (Floor 2)
Lv 6 - Cure-All (Floor 3)
Lv 5 - Erase (Floor 4)
Lv 6 - Extractus (Floor 4)
Lv 5 - Healus (Floor 5)
Lv 5 - Reflecta (Floor 5)
Lv 6 - HP Max Up (Floor 5)

Again, none of these can be missed for good. You can buy them later.

Notes:
The clock stops during the Moon Laser game, and the boss fights subtract a fixed amount of time. The first and second floor bosses take 12 minutes and the fourth floor boss takes 6 minutes.

If you would like to explore Nene's Fortress at your own pace, there is another strategy. Just keep an extra save file at the beginning, and run through the fortress without worrying about anything but speed. When you get to the end the achievement unlocks. Now go back to the beginning and move through the dungeon slowly collecting everything. It does not matter if you take longer than an hour, you do not get a Game Over. The only thing it affects is the achievement, which you already got. It's not really worth it in my opinion, but go ahead if that's what you want to do.