I didn’t have much luck with the AI picking reinforcements as its superweapon until I reached the rank of Vice Admiral (approximately 175 ships sunk). After I reached that rank it seemed to choose that as one of its superweapons almost every game. You won’t know if the enemy has chosen reinforcements until you hit the reinforcement ship. It will show up as a sixth ship down in the bottom left corner of the screen. You can see what that looks like in this screen shot:
You’ll need to go ahead and complete the game after you sink the reinforcement ship for it to save. Once you sink the fifth reinforcement ship the achievement should pop immediately.