To promote a pawn, you have to reach the opposite side of the board with a pawn. This can sometimes be easier said than done, as there will be fewer pieces due to this being a late-game strategy, your opponent won't usually let you promote a pawn as you can use it to get a second/replacement queen.
Chess is too complicated of a game to provide a walkthrough that doesn't require a friend who is willing to throw a match for you so that you can get this achievement. When you're at the point where you're selecting an upgrade for your pawn, resist the temptation to go for a second/replacement queen and select one of the other options from the piece selection and you'll unlock this achievement.