World Map Changes
Once you obtain Ultima, the World Map undergoes a number of immediate changes. With a few exceptions (the Snow Field, Deist Island, the Tropical Island, and the Mysidian Tower Area), all World Map Random Encounters have been changed to much more dangerous versions. Your next task is to return to Castle Fynn, so for the moment you only need to worry about the Ocean and the Fynn Area.
The Ocean is now filled with the same Monsters as you fought within the Leviathan. Bolt Fish are still best fought with physical attacks, while you can deal with Sea Dragons and Manta Rays with Lightning. Your biggest concern is being pelted with abilities that dish out damage to the whole party, such as Thunderbolt and Tsunami, but these Monsters aren't much of a threat to actually kill you at this point.
The Fynn Area, which now covers much of the early game area, is another story. Complicating things, Altair has been destroyed and is no longer a waypoint to stay at an inn. Gatrea, Paloom, and Poft have all suffered the same fate. On the upside, most of the Monsters here (with one notable exception) don't present a large threat. The only exception are Sorcerers, who appear quite often and in large groups with Captains and Sergeants. The resistances on some of your new equipment will help against their Status Ailment Spells, but enough of them will still cause problems. It may be worth fighting a few of them now to earn a Haste Tome, which they will generously drop 10% of the time.
The Cyclone
The cause of all these changes is the appearance of the Cyclone, a mobile dungeon that is responsible for destroying several towns and now threatens Fynn. The soldiers in Castle Fynn will explain that the Emperor summoned the Cyclone, and that there's no way inside. Hilda teaches you the [Cyclone] Keyword. Mention [Wyverns] to her, and she'll mention that they used the light of the Pendant mentions that you'd need to be able to fly to enter the Cyclone. You'll also find Leila alive and well here, though she offers no advice on the Cyclone situation.
In order to actually summon the Wyvern, you'll need to use the Pendant on the mirror in Castle Fynn. To get there, return to the 1F and head to the stairs in the southwest corner. Follow these up to the 3F, where you'll find the mirror beyond the door at the end of the western hallway. The Wyvern is an interesting Key Item, as it can be used in battle for a free Blaze 7 effect. It makes sense to give it to Ricard, both because it's story appropriate, and because if he still has it when he leaves the party, it will free up an inventory slot!
Paul's Treasure Room
Before you leave the area, return to Fynn town and speak to Paul. If you mention the [Cyclone], he tells you to search next to the bed. Take his advice, walking through a false wall on the eastern wall next to his bed, to find a Treasure room. Nothing here is new, but there are several great treasures you could use another one of. Chief among these are a second Blood Sword as well as another Gold Hairpin. Another set of Black Garb may also be of use, depending on your party setup. The rest of the Treasure can be purchased, and includes three tiers of cuirass, an Elixir, and Thief's Gloves. When you're ready to leave, step through the middle of the western wall.