Head back to Poft, then buy the airship ticket to Kashuan Keep.
I also highly recommend you buy at least one "Cottage" in Poft because we'll venture into 2 dungeons without any towns nearby.
Optional Story: if you go back to Altair and report what has happened to Hilda, she'll instruct you to go to Kashuan Keep immediately. Hilda and Cid will be waiting outside the Kashuan Keep.
Bestiary:
Head straight north to the door (A).
Examine the door and choose "Key Items -> Goddess's Bell".
Enter the door, talk to Gordon, the man blocking your path. He then joins the party.
Proceed to the next area (B).
- C-032: Cure Tome - Bottom-left corner, after Gordon joined the party.
Proceed to 2F from the stairs (C) in the bottom-left corner.
- C-033: 500 gil - Top-right corner.
Keep following the path and take the exit (D) to the next floor 3F.
- C-034: Golden Shield (Monster) - Bottom-right corner. Monsters: Wererat x5
Follow the path and take the exit (E) to 4F.
Only the middle-top room (F) has treasure chests.
- C-035: Mythril Axe - Left chest.
- C-036: Werebuster - Middle chest.
- C-037: Mythril Sword - Right chest.
Continue to 5F (G).
- C-038: Golden Armor (Monster) - Chest in the middle.
Monsters: Mine x4, Balloon x2
Top-right room (H) has 3 chests:
- C-039: Mallet - Left chest.
- C-040: Antidote - Middle chest.
- C-041: Eye Drops - Right chest.
Take the staircase in the bottom-left corner (I) to go back to 4F.
Enter the door (J) to your left.
Heal up, make a quick save, and prepare for a boss fight.
Boss: Red Soul
This is an easy battle. However, the boss can absorb almost all magic attacks, so use physical attacks to kill the boss.
- C-042: Egil's Torch - Chest behind the boss.
Now you can use the "Teleport" spell to exit the dungeon.
Note: using Teleport consumes your HP, so you should heal up after.
Re-enter the Keep, then examine the fire in the middle. Choose "Key Items -> Egil's Torch". Exit the Keep.
Optional Story: if you go back to Altair and talk to Minwu, you'll learn that Hilda has been kidnapped by the Dreadnought.