The story of Amazing Penguin revolves around a penguin protagonist navigating through 40 levels, each consisting of multiple lines that make up the playfield. The game's objective is to fill all squares by activating switches and clearing lines, while avoiding enemies that try to stand on them.
Gameplay in Amazing Penguin focuses on action and adventure elements as the player controls the penguin protagonist, aiming to clear the playfield by flipping switches and eliminating enemies. The game features a time limit for each level, and the player loses a life if they touch an enemy or fail to complete the level within the allotted time.