This is one of two quests unlocked after completing the "It's a Start" quest. To start it, you must head to Santanillas and speak with Padre, whom you will find on the beach along with two Spanish soldiers.
Edward tracks down Maynard's Fleet with help from Padre's old crew.
After the cutscene, you return to the helm of the Jackdaw. Sail northeast to the area marked on the map. After a moment, you should reach a few Spanish ships - these will be two Schooners and two Brigs.
Continue sailing forward, and soon six British ships will appear - two Brigs and four Cutters.
Due to the number of ships, the battle can get a bit chaotic. Focus first on the small ships, which should be quick to sink, and then deal with the Brigs. If necessary, you can use them to heal the Jackdaw as these six ships are not all you need to sink. Be prepared for pirate hunter ship to join the fight and hunt you down as well.
As soon as the last ship of this group of six goes down, another wave arrives. This time, you face five ships: two Frigates, two Cutters, and a Schooner.
Using all the means at your disposal, destroy all enemy ships. Once all of them sink to the bottom, this quest will end. That was not the entire armada, but merely a small fraction of it.
After completing this quest and the "I Just Want to Talk" quest, the "A Cockalorum" quest will start automatically.