Hmm...
Here's my idea for a mini-game, sadly, it could probably only be an option at the beginning of the game before the main quest, or possibly as a "Link has a flashback mode" if it is made an option for any-time...
You go into the training hall and Eagus asks you if you want to brush up on your sword skills. If you select "Yes" you get an option not unlike the Thunder Dragon's boss-rush, only this is you remembering your lessons with fellow students.
The first fighter is Fledge - easy to win against as he is both slow and weak. (He tries, the poor kid, but Link outranks him).
The next is Groose - A very heavy hitter, does a lot of heart-damage with his blows, but much like large-built characters tend to be in fighting games, a bit slow. The key to victory against him is speed and agility.
Up next is Karane - A light-built lady-fighter, she is almost the opposite of Groose - the "fragile speedster." You can get her with some well-timed strikes, but good luck, as she's quick and good at dodging.
After that, Pipit - An all-arounder, much like you. What TV Tropes might refer to as "The Mario" - the all-around balanced in speed and strength "tough" character.
The final mini-swordfighting game boss? - ZELDA. For once, appearing not in a dress but in pants, mail and a fighting-tunic (purple or pink, perhaps? She is Zelda...) Zelda winds up being your toughest opponent, which perhaps even plays into the story a bit. Sure, she's helpless without Impa on the Surface, but that's only 'cause she doesn't have a sword! Training with her is what has enabled you to be a tough hero!