Stage 27 is the "true end" of the story.
To reach it, you must first beat Stage 18 or 19 (more likely both, to level yourself up), then return to the end of Day 1 and listen to Archimedes to unlock Stage 20 and the third version of the story. Play through these newly unlocked stages to reach Day 7 again and fight the final boss one more time.
If you felt that the final battle was a bit underwhelming in Stages 18 and 19, you'll enjoy this battle more. The boss has additional forms now, so don't waste your Moon Drive or Noble Phantasm on the more familiar form.