I guess that only "repairing the Jackdaw" means plundering.
Because you take everything from the enemy ship that is of use (plundering), instead of letting them go to lower your wanted level or adding the ship to your own fleet.
As I checked yesterday I had 80% completed. Then I tried to sink ships, to put them in my fleet and to lower my level. None of this added to my progress.
But as soon as I repaired the Jackdaw, the tracker went up.
6 or 7 ships later the achievement popped.
So you really have to repair the Jackdaw 30 times by taking over enemy ships.