This page offers a guide on grabbing the Shine Sprite in Episode 4 of Noki Bay. This area is accessed by looking into the sun near the Shine Gate once you’ve collected 20 Shines back in Delfino Plaza.
You’re greeted by a Noki as you start this Course who will give Mario a diving helmet along with create a rope shortcut up to the Noki elder who will brief you on Eely-Mouth. Take his advice and leap into the waterfall to find yourself at the sea floor where the mighty Eely-Mouth awaits.
You’ll find yourself high up here with Eely-Mouth lurking at the bottom, launching up poisonous bubbles that will inflict damage on Mario should they strike him so be sure to evade them. Additionally, take stock of the Coins around the arena, your Life will drain over time so be sure to replenish it with these Coins to avoid an early demise.
As for the battle itself, the objective is to clean Eely-Mouth’s teeth by using the Hover Nozzle above them, the only inconvenience however is that Eely-Mouth will attempt to suck you in as you approach him so be sure to not linger about for too long. Once he’s finished inhaling, the mouth will close and he’ll sink back to the sea floor, starting the process from scratch. Keep up the pressure, clean all of the teeth and eventually you’ll get your reward, another Shine to add to the collection.