I followed EvoHero's solution and it worked to a tee.
I just want to add that if you're playing single-player, you will not be penalized for killing your AI partner. Playing as Clayface, for instance, I accidentally killed my AI partner (The Riddler) twice. I feared that this would prevent me from receiving the achievement, being as how to complete the mission, from time to time I assumed control of The Riddler.
As it turned out, there was no need to worry. When I controlled Clayface, I didn't die; when I controlled The Riddler, I didn't die. And thus the achievement still unlocked, even though I killed the Riddler twice when I wasn't controlling him.
In sum, don't worry if your AI partner dies, whether at your own hands or the hands of the enemy AI; just focus on keeping the character you control alive.