Meter Burn Specials are difficult to time, so this may take some practice. You'll need at least one segment of your Super bar. Then, press Back, Towards,
to start the Lasso of Truth animation. As the lasso is about to hit the opponent, that
is when you want to hit
to turn it into a Meter Burn. You'll know you're successful when the lasso glows a little and your opponent takes increased damage.
Since you'll have to wear down your opponent anyway, feel free to try out the timing several times during the match, just be sure to save one Meter segment for the win. Once he's very near death, use the technique above to finish him and get your achievement.