Zapfish are yellow electric-producing fish that are the goal of the Hero Mode missions.
They seem to derive from electric catfish, sharing the face (albeit exaggerated and cartoonish) and the whiskers. The little bulb from its head is likely calling towards its ability to conduct electricity, but it gives it some resemblance to anglerfish along with its body distribution.
The Great Zapfish resembles actual electric catfish even more, sharing more resemblance in shapes and color though it's much bigger.
They are captured by the Octarians to power Octo Valley. Each level contains one at the end for the player to collect to finish the level. These Zapfish are initially trapped in a protective field of some sort which can be broken with a few shots of paint. After it is collected, the player's Inkling holds it in a pose on the level completion screen.
After completing a level, the Zapfish will be replaced with a plushie version. The completion pose is different too.