You can catch the parrot with a cracker (at the upper left inside Petey's Pirate Pub).
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
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.
YOURSELF! Stand on it long enough to satisfy the parrot
On top of the barrels inbetween the first house and the trading post.