Only the Grouper needs to be harpooned, despite what any quest text might say. Swordfish can be caught either way, so catch the two Grouper first, then finish the rest with normal fishing if desired. Everything can be caught safely and quickly in the area around Nada Island.

Note that harpooning requires the use of a fishing boat only, unless they changed that. Empty out the cargo hold, deploy, then remote check-in at Port Ratt if you desire to do this quest for some reason. The Marketplace manager in Port Ratt may have harpoons for sale, if needed.