No this isn't like, an actual fight. Its moreso Link fighting his inner demons and the legal system as he fights over custody of his 3 kids during his divorce with Zelda.
A little background info for everyone: After defeating Gannon and sealing him away for good, Link and Zelda decided to get married. They have been married for 10 years, but it gets darker.
Just a few weeks ago, word has it that Midna somehow came back and the Hyrluian tabloids had caught Link and Midna in a nice romp with Falbi of the Falbi's Flight-by-Fowl gamehouse on the shore of Lake Hylia. There was much drama and fighting between Link and Zelda. From the fighting it was revealed that Zelda had abused Magic Potion and was also quite unfaithful, as there was pictures of her with Darbus, the main hero of the Goron Tribe. This lead to race riots in Kaikairo Town and Zelda being dethroned. After all this mess, Link left Hyrule Castle and is now mostly seen drifting drunkenly around Castle Town. Zelda meanwhile is still allowed to live in the castle, but just as a servant and rumor has it, her Magic Potion abuse has gotten worse.
No the main point is that Link and Zelda are now in a court of law and you the jury must decide the fate of Goro, Shaniquea, and Ransont. Should it be the washed up former Hero of Hyrule or should it be the princess-turned-drug-abusing maid?