Be the Best Trainer is the title of a long series of side quests focusing around befriending dolphins in Endless Ocean 2 with the help of a dolphin trainer named Finley. It is unlocked once the player trains one of their previous partners (the Short-Beaked Common Dolphin with a golden tail or the Spectacled Porpoise that was trapped inside of Iceberg Cavern) to level two, using the Dolphin Bell on Nineball Island.
Albino Bottlenose Dolphin
The Albino Bottlenose Dolphin is unlocked in the second stage. After performing in three dolphin shows for Finley, he will tell of an albino Bottlenose Dolphin he claims he is going to befriend. At Cross Rift, the dolphin is seen trapped by an aggressive Tiger Shark, similarly to how Oceana was trapped by one near the beginning of the game's main story. Once you use the Pulsar to calm the shark down, it leaves, and the dolphin becomes your partner.
The Red-Tusked Narwhal is befriended after holding three or more dolphin shows. Finley will return to tell you about a narwhal with a red tusk. To befriend it, you must take Oceana to a specific hole in the ice in the North Coast of Canada area during a snowstorm, go ashore, and wait for it to surface for air, looking for its distinctive red tusk. Once you see it and dive back into the water with the right timing, you can befriend it.
The Flower-Patterned Beluga is befriended after 20 more dolphin shows or training dolphins 100 more times.It is befriended by using the Sea Whistle to respond to its vocalisations. This is one of the easier dolphin partners to befriend, as players have reportedly just spammed using the Dolphin Bell until they have trained dolphins one hundred times to unlock the quest.
X-Scarred False Killer Whale
The False Killer Whale with a strange Scar is only befriendable after you have befriended the odd Beluga, and Finley comes to tell you about it. He says that it was seen in Valka Castle, so once the player goes to the Castle, they can find this specific False Killer Whale.
It flees from the player at first, but if you chase it all around the Castle, eventually you'll be able to use the Pulsar to calm it down. After that, it will become your partner.
Pink Amazon River Dolphin
This All-Pink Amazon River Dolphin can only be befriended if you let it interact with the red-tusked narwhal the player had befriended previously. You can find it in the Twilight Temple with the other Amazon River Dolphins.
It is the only dolphin partner that is able to open the Queen's Lake, as it is the only freshwater dolphin partner.
Pacific White-Sided Dolphin With Weird Dorsal Fin
This specific Pacific White-Sided Dolphin has a white dorsal fin, and is befriended after approaching it multiple times over the course of a few days, as it is very shy and will only warm up to the player if they approach slowly. Once Jean-Eric says that it is okay to touch the shy creature, the player will do so, and the dolphin will be your friend.
The player can find this dolphin in Deep Hole with the others of its kind.
Hungry Risso's Dolphin
The Small Orca is befriended by giving it a toy float, also bought from Nancy. The player figured this out because, due to a specific set of markings on the whale, Hayako identified it as one she knew when it was in captivity once, and remembered that it liked floating things. It can be seen near other Orcas in the Zahhab Region.
The Commerson's Dolphin with strange, scrolling markings is found in the Treasure Room in the Cavern of the Gods. It will 'speak' to the player, demanding offerings from them for the "gold lady" (the Pacifica Treasure), all of which can be bought from Nancy. Once you complete its requests, it will become your friend.
Finley will simply declare you and himself "Eternal Rivals" once you have befriended all 11 cetaceans.