The main antagonist of Tomb Raider II is Lara Croft's former lover, The Tibetan , who is trying to steal the Dagger of Xian. The Barron, a corrupt businessman, is a minor antagonist who helps the Tibetan.
While you do encounter the Barron and his goons in the game, you don't fight him directly. You are mainly focused on navigating through the levels, solving puzzles, and retrieving the artifacts needed to stop the Tibetan.
If you're referring to a specific encounter with the Barron that you're struggling with, please provide more context so I can give you more specific help.