From Regole, head south, ignore the castle on the side.
Take this chance to kill Kuza Beast around the castle area for a bestiary entry (see the strategy below). Then follow the path east until you see a round forest surrounded by mountains.
Bestiary:
Kuza Beast is missable later on, so you should kill it now while you're traveling to Moogle Forest. It spawns around the Sealed Castle area. You can use Death Claw + attack or Control, then spam magic spells to kill it.
Moogle Forest
Nothing much to do here; simply talk to the Moogle, then follow him into the hole.

Underground Waterway
Because the water is flowing, you won't be able to go back upstream. So make sure that you don't miss the first chest.
Note: In case you missed the first chest, you can still re-enter the Underground Waterway by entering the hole in Moogle Forest again.
Bestiary Checklist:
Item Checklist:
- C-082: 4400 gil
- C-083: Phoenix Down

Boss: Tyrannosaur
Tyrannosaur is an undead monster, which means it is vulnerable to healing. Simply cast Raise (White Mage) or throw a Phoenix Down on it to end the battle quickly.
If you want to fight the normal way, then you can use any fire-based spell like Fira, Flame Thrower, or Ifrit, etc.