What does tug-of-wills means as no definition can be found through Internet?

You're right, "tug-of-wills" isn't a standard English phrase. It seems like a playful or humorous misspelling of "tug-of-war."

It's possible someone made a mistake when writing it, or they were trying to be funny by intentionally misspelling the phrase.

If you encountered this phrase in a specific context, please provide more information so I can help you understand what it means.