Nothing embarrassing at all!
Actually, there is already the "Fantasy Battle Mode", a game mode unlockable after beating the game, in which if you complete this special Boss rush, you can get all the missing special equipment in your cleared game!
This not include the secret boss battles or weapons acquired from them though.
So if you missed them, you would need to start the game from the beginning.
Consider that across the game there are different dialogs and events depending which girl you chose to start with, so starting again the game again doesn't get boring or too much repetitive.
So if you finish the game and still want to experience the things you missed, I suggest to start a new file with another Myth leader!