Battle vs. Chess

I unlocked this achievement in a Classic Skirmish game. It cannot be done in Head to Head mode (as with most other achievements). It doesn't matter what colour you are.
I put the difficulty at 0 also to make this easiest.

I'd play the game normally until the message "Opening Book mode is finished, you're on your own" comes up which will be in the first few turns depending on whether you make a standard opening move or not. The opening moves will be in blue circles.

Then way I did this was using the hint (RB) button every turn and choosing the Queen or whatever piece was in the enemy king's vicinity or could be threatening to the enemy king. The hint moves will be shown in Green circles.

When using hint, the game will suggest multiple moves, most of them are good moves so just pick the best one which would help the game progress quicker.

The enemy king will most likely castle King's side so you'll be focusing on the F, G and H columns. Try and weaken the pawn defense in front of the castled King.

The AI is still pretty smart despite the difficulty being at its lowest so keep an eye on your own defense and watch the enemy's moves if it is not trying to stop whatever you are doing.

As long as the game finishes in less than 5 minutes, the achievement should pop.

Best of luck.

EDIT: You can also boost this achievement online with another player, slipped my mind.
Thanks acedawg :)