I recently read an article about one of our most strident supreme court justices, and they said he had a "take no prisoners style." What exactly does that mean?

That means they learned their craft from Torquemada and Machiavelli. Alito, Scalia, and, to a lesser extent, Thomas come to mind.

What exactly does [a "take no prisoners style"] mean?

From Wikipedia (link): "In modern usage, “take no prisoners” is used in a political sense, referring a person’s political approach, styles of written and visual arts, and speaking abilities. A politician who delivers an aggressive and vindictive speech against an opposing party might be considered to have a “take no prisoners” attitude." It's from the military usage where it is meant literally.

I hadn't heard it used before. While I did read about it, I always learn more from people who have used it. Thanks, z!