While Circle of the Moon does not have explicitly defined chapters, there is a logical division marked by boss fights. There is an order in which you go through the the castle, however some areas are optional. You will always be able to (and in several instances, have to) return to previous sections of the castle in order to get power-ups that were originally inaccessible and in order to reach new areas of the castle. In most cases, once you defeat the local boss, you'll receive a relic that will give you a new ability, which makes exploring the next area possible (or at least easier).
The Underground Gallery, Underground Warehouse, and Battle Arena are option areas. The Gallery and Warehouse each contain several power-ups, as well as relics that will make future areas easier, allow you to get quite a few power-ups from old areas, let let you fight the three winged demons - all of whom give you a lot of experience and powerful tools. Note that you must finish the Underground Gallery to access either of the other two optional areas.
On that note, you can begin your journey. At the bottom of a pit, no less...
Notes & conventions
When applicable, each section of the walkthrough will begin by pointing you to important equipment, power-ups, and new enemies that are now accessible in other sections of the castle.
It will be assumed that you are completing all sections of the game in the order specified. Should you choose not to complete a section, it will result in you being unable to retrieve certain things or enter certain areas. Simply skip over these sections. It is highly recommended that you do not sequence break your first time playing, as doing so makes the game substantially harder.
At the beginning of the main section of each page of the walkthrough, there will be a sidebar listing important items that you can collect between the time you first enter the area and defeat the boss. Items that you have to come back for later on will not be listed.