Don Mattingly had a beautifully simple swing that was also very effective. It was also completely different than the A to C Swing that Don Mattingly now advocates. Baseball would be much better off if Don Mattingly taught, and people studied, the swing he actually used.
Elsewhere, I go into The Secret of Don Mattingly's Swing, but here are some clips of Don Mattingly's swing and a high-level explanation of why Don Mattingly's swing was so effective.
Don Mattingly
Don Mattingly
Don Mattingly
The thing to pay attention to in Don Mattingly's swing is how, rather than staying upright and keeping the barrel above the ball, he instead Tilts over the plate and swings with a Slight Uppercut. That allows him to match the plane of his swing to the plane of the pitch and maximize the likelihood that he will make solid contact with the ball.