The Cardinal seems to be getting rather dishearted about your continuing failure in rooting out any Templar agents. Since he doesn't have any further tasks for you at the moment, he suggests you speak to one of his colleagues.
- Board the Inquisition Flagship
- Do Not Sink the Inquisition Flagship
- Prevent the Pirates from Defeating the Flagship
Before your obligatory visit to Mogens Brisebois in Tortuga, you will first have have to go and see Henrique Ruiz. He will tell you about a high Inquisitor that's coming to town. Take this news to Brisebois to get your mission briefing: he plans to embarrass the church by staging a pirate attack on the Inquisitor (spreading rumors about a treasure fleet will see to that). In the ensuing chaos, you have to board the flagship.
The main part of the mission has you alone with 15 enemies, all between level 34 and 36 (with the exception of the flagship). But don't panic, they won't be interested in you unless you attack them or get in their way. Your opponents in fact consist of five different fleets of three ships each, and they're all locked in one big battle. There will be three Inquisition ships and four different pirate gangs attacking them (and each other).
At the start, hang back to watch the carnage, but be careful to keep a close watch on the Flagship, because it has to survive. Fortunately it can take quite a beating (it's a level 60 'San Mateo' Heavy Galleon), but you don't want to cut it too close. After it's defenses have been softened up a bit, move in and disable its masts, then try to bring the crew down as much as you dare (remember, level 60) and board as soon as you feel you can win the boarding combat (by now some of the pirates should have started attacking you).
By the time you've finished the boarding combat and are back on your ship, most of the pirates should have sunk each other. You can stay for a bit of extra xp and loot and finish off the survivors, but it's not necessary for the mission.
Unlike all the previous missions in this chain, you actually claim your reward for this one from Mogens Brisebois. You will still have to go back to Santiago to get the follow-up from the Cardinal, though.