To do that you have to first shoot it down with a siege weapon of sorts, successfully immobilize it, and board it via the skiff. Which should then trigger the said objective after loading in the tile.
We have raided (please don't let the navies see this) at least fifteen merchant ships that session and the objective stayed like so, unfinished after all that.

This is of course done in the Surface server and I am playing with the PC platform.
Thank you for your time.