Now that you have access to your ship, try to kill Sea Dragon (#112) on the Surface World's sea. After that, go back to Gysahl (Floating Continent) to check your bestiary list below:

Floating Continent - inner sea:

• [FFIIIR-031] 031. Killer Fish
• [FFIIIR-032] 032. Hermit
• [FFIIIR-033] 033. Sea Elemental
• [FFIIIR-034] 034. Tangie
• [FFIIIR-035] 035. Sahagin (rare encounter, I found them on the sea between Viking Cove and Nepto Temple)

Floating Continent - outer sea:

• [FFIIIR-071] 071. Anet
• [FFIIIR-072] 072. Mermaid
• [FFIIIR-073] 073. Seahorse
• [FFIIIR-074] 074. Sea Serpent

Surface World's sea

• [FFIIIR-112]112. Sea Dragon

Once you have collected all of them, it's time to move forward with the story.