The Fighting Mode is a special mode, only available to the Directors Cut version, adn the U.S and European Version. To Unlock the special modes, you need to complete these requirements.

1.Explore the Aquatic Garden of Surferio.
2.Obtain the Paracelsus's Table at the end of the dungeon.
3.Show the treasure to Craftsman's Guild in Peterny.
4.Go to Peterny and choose to go to the fighting arena.

Yes, You always Have to go to the Craftman's Guild in Peterny, but the Travel is worth it.