When the parrot says : "jump in the sea", he literally means that you have to go dunk yourself. The easiest way is to dive past your ship and swim back to the beach alongside the pier.
To get the map piece :
parrot port.
If you look at the island in the middle it is to the right of it
Parrot Port
The only time you dive in on purpose is to follow the instructions of the parrot at Parrot Port. When you jump into the water and return, the parrot has moved to a higher window. (see related question)
When you are talking to the parrot at Parrot Port, he will tell you to jump in the sea, which means jump in the water. When you return, he is higher up on a Trading Post window.
Usually Parrot Port, for between 32 and 40 doubloons.
It is the island directly to the right of Fort Ridley, in the 3 o'clock position on the island map.
It's on top of the pub (on the chimney).
You find the navigator in the second floor of the bar at parrot port.
Parrot Port has the highest price on medicine. It is the island in the easternmost island.
Parrot Port- it is the island to the immediate right of Fort Ridley
At Parrot Port, the "vent" is the chimney on the roof of Petey's Pirate Pub.