Thalassophobia is the fear of the sea/ocean, I couldn't find a name for the fear of sea monsters.
I don't think it's silly at all. Thinking about how huge/deep oceans are and how many of them we have, some things have been discovered that for years we never thought possible. It's arrogant for the human race to think that we've discovered everything there is that needs discovering.
Not that I'm necessarily saying that the Hydra or anything like that exists, but there are some strange, massive things that live deep down in the ocean, and hey, not even that far down, I mean Sharks are pretty damn scary if you come across one, who's to say that isn't a sort of definition of a sea monster?
Thalassophobia is fear of the sea.
Ketos means sea monster but it also means whale. Basically it was anything big and somewhat fish shaped. In the myths it was usually depicted as a long serpentine fish with long rows of teeth. Ketophobia could get you closer to the sea beast meaning but Cetaphobia is a fear of whales. It is actually somewhat common.
Therophobia is the fear of beasts.
In Greek mythology Thêr Thalassios were "monsters of the deep". So maybe therothalassophobia? I'm not sure. I am not practiced at mashing greek words together. It is a guess though.
Terato means deformed or monster. So yes, teratothalasso phobia, fear of sea monsters, works too.
"Ridiculous" would be my guess.