The Cardinal now wants you to publicly arrest a certain Pirate Captain who isn't very popular among his fellow pirates. At the same time, you are to loudly accuse him of being in league with the Templars.
The Empty Gibbet, Tortuga Inferno
Again, you will first have to talk to Mogens Brisebois in Tortuga first. He won't mind you arresting that pirate, but asks you to be not quite as loud about the Templars as the Cardinal wishes you to be.
The main part of the mission takes place in an instanced version of the tavern. You'll have to fight a swashbuckling duel against a single level 36 Lieutenant-rank NPC, who will surrender once you brought his hitpoints down enough.
- Arrest Archibald Ironfoot