Just like World at Arms, you can abuse the revenge trick.
Wait until you are attacked and lost the battle. Go to your headquarters, choose reports, and choose a revenge battle against the attacker. This will cost you 4-6 faith. When you get to the screen where you choose your troops just quit the game by holding the back button and closing the window. Don't use the normal way of quitting. When you load up the game again you will have gotten credit for a revenge attack, but you will have the ability to attack the same foe again. Rinse and repeat 10 times and you will get the achievement. Keep in mind that you will lose the 4 -6 units of faith every time you do this.
If you're having a hard time getting someone to attack you, you can follow neeker75's advice and get a Facebook friend to help:
"You'd need to be Facebook friends with one another. Go to the fight screen, and click the top right corner to bring up the "Tools" menu. Go to the "Friends" option here, and login to Facebook. Your Facebook friends playing this game will now show up as your allies. They can attack you from here (and vice versa obviously). Upon getting beat, you'll get the revenge option in HQ. From here, just follow MrZombieChicken's guide of holding back button on phone, and closing the window there to quit 10 times. Do note that this cost me 6 energy per attempt. "