After you train your dolphin so well that it reaches level 2, you can meet Finly the "World's Greatest Dolphin Trainer." After you get him to see your Dolphin Show. After he sees it he will tell you to go to Ciercos Strait, to find a white Dolphin. It's a Albino Dolphin. Rescue it from a shark and you will befriend it.
Apollo the Ocean Sunfish
If you go to Deep Hole at night (beware of tiger sharks!) you should find a large golden ocean sunfish somewhere above the Mouth of Truth. It is the legendary creature Apollo.
Big Bob the Penguin
In the Weddel Sea, on one of the landing spots you will find a REALLY BIG EMPEROR PENGUIN. Scan Big Bob to get his info.
Golden Catfish
Once you find the Servant's Ring, eventually the large catfish in front of the building in Cortica River will come up to you. It will say it likes your ring. Give it the ring and return to boat. Return and the catfish will be gold.
Legendary Turtle
If you have Snorkel on the Island, look for him by the bonfire. If you pet him, he will point out a strange moving Island out in Gatama Atoll. Investigate to find a huge, legendary leather-back sea turtle. You will receive a new title for finding him.
Okeanos Guardian
Scan the largest shark in the temple of the gods when you face off against the goblin sharks to get Okeanos Guardian.
Pelago Crocodile
To find The Pelago Crocodile you must look through your telescope on the morning before the full moon. Hint: Keep on entering the cabin to skip to the sunrise.
Phantom of Valka Castle
Go to Valka Castle at night with Oceana and the "Ghost" will be there.
Pygmy Sperm Whale
Go to the Mouth of Truth, go down to the bottom and you will see some rocks blocking a path. Make sure you have one of your dolphin friends with you, and once you move the rocks a pygmy sperm whale will come out of the cave.
Sea Serpent
If you have sold over three Maps, Oceana will mention a shadow on the map of Ciecrocos Strait, it is the Sea serpent. Keep asking Oceana about it and she will tell you where it is.
Singing Dragon
After you have gotten past the Giant Goblin Shark in the Cavern of the Gods, a white whale appear before you. It is the Singing Dragon.
Snorkel the Lab
If you look through the telescope on Nineball Island you will get a tip about something washing up on a beach in Gatama Atoll. Travel to the northeast section of the map and go ashore to find a shipwrecked Labrador Retriever. You can bring him home as a pet and Oceana names him Snorkel.
Trident Ring
At the middle level of Deep Hole in Gatama Atoll, there is a small cave in the floor with a ribbon moray inside of it. Use the multisensor and you will discover a small ring, called the Trident Ring, worth 9800p.