Pearls can be obtained from oysters found deep in aquatic environments. Oysters naturally produce pearls over long periods of time, and are unwilling to just hand them over.
To get pearls you must first tire out the oyster by repeatedly provoking it into attacking you. After 3 consecutive attack attempts, the the oyster will tire and open up upon the fourth provocation, letting you simply take the pearl.
Can be found at:Edit
Aquatic Planet: 110-250 depth
Here after the oyster tire: