The easiest way to beat the computer at Nine Men's Morris is to simply trick it into playing another computer. Choose to go second, and input the computers actions as your own in a second game of Nine Men's Morris.
Make sure the computer level is set to the highest in your second game, and just do whatever the computer does in your first game. You'll effectively be acting as a means for the computer to play itself, but you'll almost definitely win the "Assassin's Creed 3" variant in the first try.
I recommend using Paul Emory Sullivan's Nine Men's Morris for several reasons; notably, it is easy to access, and I can personally vouch for it. I used this solution to unlock the achievement several years ago. I have provided the mobile version, as it is by far more accessible. You can see the full version here.
Ultimately, it shouldn't matter what version of the game you use; as long as you have the option to compete against a high-difficulty computer player, it should have the same results. Nine Men's Morris is an ancient game that dates back as far as the Roman Empire; much like Chess, the rules do not change.