Did you look at the list of Book 3 side quests, or did you look at the list of Monquista quests? There is a quest given by Sancho Panza in La Mancha after you turn in the Monkey's Paw to the queen. It can be overlooked easily if you do not return to that area.
The Pirate101 Central Wiki says that there are 13 Chapter 4 Side Quests and 1 Chapter 6 Side Quest to complete for the Pirate Gigante Badge. I am guessing that you are missing the Chapter 6 Side Quest "Vanquish Them" which you can get during the Quest "To Avernus, and Beyond" after talking to Gortez. You get Vanquish Them from Pancho Stanze in La Mancha.