Final Fantasy II/Mission to the Colosseum

You'll need to return to Altair to continue. From Deist/Bafsk, you have some options. Due to the weird nature of the map, you can either begin sailing due north until you cross the northern/southern hemisphere boarder and travel up the sea until you arrive at Altair from the east, or you can sail to the east, crossing the eastern/western hemisphere boarder, and travel across the land until you return to Altair. As usual, consult the map to prevent yourself from getting lost.

Altair
Once you make it back to Altair, all anyone seems to be talking about is how strange princess Hilda has been acting lately, laughing whenever people speak to her. Speak with Gordon and he will express the same concern, asking you to speak with her to see if everything is alright. Princess Hilda can be found in her room, which is located directly below the king's chamber. (Before you enter the room, unequip Leila's equipment if you do not want to lose her equipment as she will leave you after this sequence.)

Hilda will invite Firion to speak with her in private, so your other party members will leave. The princess tries to seduce Firion who, wishing not to be rude, steps closer at her request. When he does, the monster who was impersonating Hilda reveals herself. At that point, Firion's companions burst through the door to aid him in the fight.

The monster is a Queen Lamia. She has a powerful attack that not only causes a lot of damage, but also puts its victims to sleep. You'll need to doll out Cures to anyone who gets hit, but you may also wish to have the Basuna spell ready to go in case too many members of your party fall asleep. In addition to all of this, she has the power to cast a level 16 Blink spell, making her nearly impossible to hit physically, and a charm spell that can turn your party members against one another. After she is defeated, a guard and Gordon will enter the room. They have discovered that the real Princess Hilda has been captured by the Emperor, and he is offering her as the prize at the Arena's fight. Gordon will insist on accompanying you, so Leila will leave you in order to assume Gordon's duties around Altair.

You will hear reports that the Arena is located in Palamecia, which can be found directly south of Kashuan Keep, through the desert. However, there's a far easier way to find Palamecia; simply travel north west from Altair and approach the desert from the south. You'll find the Arena off to the right side of the desert.

Arena
Enter the Arena and you will find yourself trapped by the Emperor. He will trap you in the arena area to fight a monster. After you defeat it, you will head towards the Emperor but he will disappear and set his soldiers upon you to capture you. You get thrown into jail but someone will come to release you for helping him escape from the mines. Search all the rooms within the area to gather all the treasure boxes and go upstairs from the top right corner.

Unequip Gordon before you enter the room containing Princess Hilda as he will leave with Princess Hilda after you open the door. Leave the Arena and head back to Altair to find everyone gone.