The game has for stages, with each stage containing 4 levels/acts. There’s a boss waiting in the fourth level/act. You have to defeat it in order to proceed to the succeeding act. The last stage in Story Mode will pit you against two bosses consecutively.
Each stage has 4 acts. You can create a temporary suspend save file to save your current progress. When you load this save file, you’ll start at the beginning of the level. After completing the Story Mode once, all other game modes will be unlocked, allowing for more replayability.