In the Sumo variation of Sorry Sliders, there are three large blue Buddha-like statues added to the board. They can be knocked around just like the regular sliders. Knock them into the green "Sorry!" zone around the outside of the board, or let the computer player do it.
For me, the achievement unlocked as soon as the statues were completely within the green area. They don't have to finish the round or the game in the green, just get knocked there.
Hit the statues at an angle (as the computer player so often does), not directly head-on, to improve your chances of knocking them to the outside of the circle.