Zebes is riddled with secret passages and hidden rooms, many of which contain valuable power-ups or lead to shortcuts. The most common way to find these is by using Bombs (acquired with the Morph Ball) on suspicious blocks. Look for blocks that appear slightly different, have unusual textures, or are in places that seem like dead ends. The Screw Attack can also destroy certain blocks. Additionally, some passages are hidden behind false walls that you can simply walk through. Experiment with bombing every wall and floor in rooms that seem to have no obvious exit or contain a power-up you can't reach. Exploration is key to uncovering these secrets.
