Though Jotaro is the main character of the chapter, any party member can be used to challenge the boss, and the dialogue will be different for each. Kakyoin cannot be recruited until after the jail cell is opened.
Though there are Green Hornets flying around the boat, there's no sign of a boss. Open the chest with the Cell Key on the bottom floor and head back to the jail cell on the deck, then head back to the bottom floor to initiate a battle, which will net you 1FP with your party member.
Talk to the nurse on the bottom floor to recover for free. However, after you do so, there's a chance of a random status effect being inflicted as soon as you walk out the door.
Once the orangutan has escaped from the cage, if you check the corpse where the nurse was standing, you'll notice something odd about it. If you head back to the bottom left on the 1st Floor of the ship and check one of the beds, Kate, the user of the Green Hornets, will attack. Defeat her for a Badge of Honor, and +1FP for whoever's in your party. In addition, all Green Hornets on the ship and in future destinations will vanish.
If your Stand is Adam Ant, there will be extra dialogue during the battle with Kate.
Range: M, but short-range attacks are equally effective. Random encounter on the deck. Checking the hook by the sailor also starts a battle. Weak to Fire, Electricity, and Light.
F.F. Sports Drink
Range: M, but short-range attacks are equally effective. Random encounter inside the ship. Appears with Hydrant. Occasionally self-destructs by launching itself at the party. Weak to Fire, Electricity, and Light.
Range: S. Random encounter inside the ship. Appears alone or with Propeller. Can inflict Bind. Weak to Ice, Electricity, and especially Earth, Wind, and Light.
Range: M. Having mid- or long-range attacks will make the battle easy. Defeating the Green Hornets that accompany her won't damage her, and will only cause them to respawn with full health. Weak to Fire, Earth, and Light.
Starts out at range M. Will summon a Propeller and Hydrant that will recover each turn. Invincible to physical attacks while inside the wall. If Bind status (or any status that restricts movement barring K.O.) is inflicted on Jotaro, a special scene will play and the battle will end while still giving out EXP, items, etc.