For me, completing this achievement seemed easy, but ultimately turned out to be rather annoying. You can only specifically select one character, for free play; the other guides clearly show getting around this fact with a second controller, but what do you do if you do not have a second controller?
I found a rather simple and quick solution. After unlocking Count Dooku and Jedi Anakin, load up Epsidode 3: Councillor in Peril, in Story Mode. You will start the level, playing with Obi Wan Kenobi and Jedi Anakin. Ensure you are currently playing as Obi Wan Kenobi, and leave back to the Cantina.
When you return to the Cantina, the computer player should still be playing as Jedi Anakin. You are now free to enter back into any level, ensuring you pick Free Play and Count Dooku. You should retain the computer player, ensuring you have both Count Dooku and Jedi Anakin in your party. Bring out both characters, and kill Anakin as Count Dooku. Easy achievement.