The Pacific White-Sided Dolphin with a White Fin is one of the Dolphin Partners the player can befriend in Endless Ocean: Blue World. It can only be found after Finley brings the odd creature to the player's attention.
This specific Pacific White-Sided Dolphin can be found in the same area as the main pod in the game: Deep Hole. However, once this specimen has been brought to your attention, a cutscene will play, showing you which one to interact with.
This specific dolphin is quite shy, and will flee from the player the first few times they attempt to approach it. It is suggested that you try coming back on different days a few more times so that it becomes used to you.
Eventually, the dolphin warms up to the player, and it will become one of your dolphin partners.
In Your Notebook
The quest relating to this dolphin is entitled "Dolphin in Deep Hole". In your notebook, it states:
"A dolphin with a uniquely coloured dorsal fin has been seen in Deep Hole. If you get the chance, try to find out more about it."
Once you see the dolphin for the first time, your notebook will update with the following:
"It's a Pacific White-Sided Dolphin, and it's very shy. Try coming back a few more times on different days."
After the dolphin decides to become your friend, the quest is finished with the statement:
"The dolphin slowly warmed up to you and became your friend!"