Talk to Explorer Vayne Ashe and she replies with:

"Please can you help us kill the Mermoths?"

Respond with "Why?"

"Because they have overpopulated the area, the result is that there us almost no fish left in the waters around here, we need the fish to feed our soldiers. Can you help us out?"

Respond with "I will help you!"

"Great! They are located on the island to the east. They are big and clumsy so killing them shouldn't be any problem."

Respond with "On my way!"

Crazy Fish says

You don't have to restrict yourself to hunting the Mermoths on the island she recommends, you can kill them anywhere on Calypso and they count for this mission. I found the best area was the small island just north east of Atami's Paradise (the Molisk Land Area).