You are now back on your airship, and whenever you attempt to land, it'll trigger another cutscene.
Okay, let's head back to Castle Tycoon for another flashback.
Castle Tycoon (Optional)
There is an optional story when you revisit Castle Tycoon. Just like before, once you enter the throne room, the chancellor will ask if you want to rest for the night; answer "Yes".
Catapult
Fly your airship to Catapult and disembark. Make your way to the Living Quarter.
In the right room, read the note on the table. It gives us a clue where they are.

Meteorites
There are 4 meteorites you have to visit in order. All meteorites have a linear path, so I won't be doing maps for each one. Each meteorite has its own boss except the first one — Tycoon.
Let's visit them in order, trigger each cutscene, and fight the bosses:
- Tycoon Meteorite
- Karnak Meteorite
- Walse Meteorite
- Gohn Meteorite

Boss: Titan (Karnak)
Guaranteed Drop: Hi-Potion
Its signature skill is Earth Shaker, which hits hard, so make sure you always heal your party.
It doesn't have any weakness except that it only has 2500 HP.
Simply spam 1000 Needles (3 Blue Mage) to kill him in one turn.
Boss: Purobolos x6 (Walse)
These guys have their trick. Basically, you cannot kill them one by one or they will fully revive their friends back. So, you gotta kill them all at once.
There are many strategies to do this:
Strategy 1: Use Zeninage (Samurai command) to instantly kill them all in a single attack (it consumes about 7000 gil).
Strategy 2: Use any AOE skills like elemental scroll (Ninja) or elemental magic (Black Magic). Combine with Silence (White Mage) to prevent them from healing or reviving their friends. Or if you prefer Bard, Romeo's Ballad works great too, to freeze them so that you can free hit until you win.
Boss: Chimera Brain (Gohn)
Guaranteed Drop: Phoenix Down
This boss doesn't have any weaknesses, but it absorbs ice, so avoid using any ice-based magic.
The quickest way is to use Death Claw (Blue Mage) and finish it with an attack.
Other than using Death Claw, you can fight it the normal way as long as you can keep everyone alive.