After reuniting, Nate and Elena proceeded to make their way to the dock, hoping that the escape boat was still there. They entered a room that contained all of the old ship manifests. After spotting a logbook that has been left on a table, Nate went over to study it. It contained information about the Esperanza, which sailed from Callao, Peru, carrying a gold statue weighing 20 arrobas (500 pounds). Upon turning the page, Nate found a detailed drawing of El Dorado, which unfortunately happened to be the last entry in the book.
Watching Nate fiddle with his necklace, Elena asked if it was from "somebody special". He explained to her that it belonged to Francis Drake and that he inherited it. Elena then read its inscriptions: Francis Drake's motto, "Sic Parvis Magna" (Greatness from Small Beginnings), as well as the date the ring was made, the 29th of January 1596, the day after Sir Francis supposedly died. Beside these were coordinates to the burial site off the coast of Panamá, left as a clue by Sir Francis. Nate then tore the El Dorado page out of the log, held it up in front of Elena's camera, and stated that it was the closest to El Dorado that they were getting.
The two continued through the building, where they soon found themselves in another firefight with several of Eddy's men. After defeating the pirates, they came out onto a balcony, where they saw no sign of the boat until Nate spotted it on the far side of the building's dock. Elena suggested that he go alone, and swing back around to pick her up, that way she could film more of the island. Nate went ahead and crossed the balcony, shortly before entering into a large, domed building where he found himself trapped.
Once you and Elena reunite, head up the stairs and proceed forward to the ship manifest room. Following the cutscene, head up the stairs and prepare for another firefight, starting with a big pirate wielding a Moss-12. This particular shootout can be difficult, as the only exit out of the room is covered by a pair of pirates on a staircase, another group on the left, another one high up on a platform, and another one on the second staircase around the corner wielding an M79. Although it is possible to make it up the first staircase for the superior position on the second floor, it leaves your rear entirely exposed, and thus it is too much trouble to go for.
As such, take down the pirates you can from the doorway, and then the one on top of the platform (if he will likely shoot past your cover), and then shoot down the remainder. After that, use the winch to open the gate to the right of the stairs and head through it. After the cutscene, shoot the lock off the door, then jump across the balcony. It will begin to crumble, sending Nate sliding downwards. Quickly tap as prompted to have Nate leap to safety.
You will then need to shoot down a few more pirates that attack you from inside the building. As you leap across the gaps in the balcony, you will soon approach a real large one, with across it a broken door right at the edge. You will need to shoot the lock off it to break it apart, then make one precise jump across the gap. Pass through the door to enter the large building, where the next chapter begins.