First of all, you don't need to keep it harpooned all the way, just let it follow the ship. It has to be able to hit the ship once per minute though or it will lose interest so slow down occasionally.
You can also do damage to it on the way, just make sure not to kill it accidentally.
Once on the shore, quickly drag it onto the beach and finish it off. It doesn't attack while beached so stamina food may be preferable for this.