These are the requirements for getting the five Stars to appear on your save file, which are needed to unlock the true final level, S8-Crown. Glittering Stars are optional, and makes your stars glitter. Glittering Stars is sometimes known as Rainbow Stars. These cannot be lost if the main game is beaten after obtaining them. Although the second star requirement may seem nearly identical to the first, this is not an error. It's probably there because some levels are optional.

Unlockable	How to Unlock
Fifth Star	Have all stages cleared with both Mario and Luigi, and have gotten a Golden Flagpole on each
First Star	Defeat Bowser in World 8's second Castle
Fourth Star	Obtain all 285 Star Medals, not including the ones from Mystery Boxes
Glittering Stars	Never have the Super/Help Item Blocks appear: Never die five or more times in a row on any level.
Second Star	Clear all stages in the first 8 Worlds
Third Star	Defeat Bowser in World 8's second Castle again after defeating him in Special World 8's Castle.