Instructions
Go to the main hub and speak to Hayako, the event planner. Select a dolphin show from the list of events she gives you. Hayako may not always have a show available for you to perform, so check back later if you don't see any in the list.
Select the tricks you want the dolphins to perform. Wait for the show to end and then collect your payment. Return to Hayako and do another dolphin show. You must perform a total of 20 shows to trigger the beluga whale event.
Talk to Hayako again after 20 shows have been performed. As you are talking to her, a man named Finley will appear to tell you about a special beluga whale that swims in the Arctic Ocean.
Select the Arctic Ocean from the location map to travel there. Choose Oceana as your diving partner.
Swim to the breathing hole in the southwest area of the map. A cutscene will play to show you where the beluga whale is located.
Focus on the pod of whales by holding down the "A" button. When you have spotted the beluga whale with the strange pattern on its back, use the directional pad to select the Sea Whistle and then press "A" to play it.
Wait for the beluga whale to come to you. When it makes a sound, blow the Sea Whistle immediately afterward. After a few whistle blows, the beluga whale will decide to befriend you. Give it a name and then go back to your base.