Easiest way is to map the serpent sightings, and prepare a trap at the nearby coast by just digging a little pond that is seperated from the open sea by a little bit of earth that you leave in place to act as a barrier and then just drag the serpent inside with the harpoon. Map the trap too to find it easily.
New Serpents should spawn at the same spot that you mapped so you can reuse your trap.

it's also possible to ram into the serpent with your ship after harpooning it which can result in the serpent getting stuck on your ship, it will stop attacking and you can park the ship in shallow waters to get all the scales. It might look very scary because the serpent head might be on top of you while you are steering the ship but it doesn't attack, apparently the Serpent only fights stuff that is in the water and it has to be in the water itself to attack anything.

Some stamina food can help a lot when dragging a serpent with the harpoon.
Also Serpents tend to spawn around those Ocean "Islands".