What is a hitting mantra?

Answer 1

I'm assuming you're talking about what is also known as "recycling". Sometimes reffered to as a trigger or thoughts to help focus on each pitch while at the plate. From my experience the "mantra" varies in length -usually about 20 seconds(the brain needs 20 seconds to refocus/recycle...hence the term recycling). A few of the top professional and collegiate hitting instructors use it in training hitters. It's used in helping the hitter become more aggressive, and driving the ball more consistently.
Some of the more common "mantras" are: Every pitch is MY pitch. Every pitch is a fastball, and I'll adjust to the curve, etc. At least these are some of the cleaner ones.

Answer 2

A hitting mantra could be defined in baseball terminology as a approach or philosophy of hitting that a player normally follows when at bat. A first-pitch swinger is an example of a hitting mantra. These batters would believe that the pitcher would normally want to start the count with a strike and would most likely pitch in the strike zone on the first pitch.

Answer 3

A philosophy to approach hitting.

Whether to "sit on a pitch" or not can be a philosophy. Or whether to swing at pitches early in the count, or try to work the pitcher.