This achievement is for completing 100 games of Chess.
Campaign missions count towards this aswell, as long as you don't opt to Restart, the game must be finished. Even if you fail the mission, it still counts.
Any variant of Skirmish Mode counts and Online play counts towards this.
All Puzzles and the Treasure Hunt challenges also count
You should get this while doing the rest of the achievements in the game because the amount of work needed amounts to about 100 games of chess.
As stated in the achievement description, don't play Head to Head mode which is 2 controller local play because they will not count.