Heroes and Villains are separated in character select. The 12 characters on the right side of character select are the villains you need to defeat. Choose Batman as your character and win a match against each of the 12 villains to unlock this achievement.
After completing Story Mode, you'll have already defeated Deathstroke, Bane, Lex Luthor, The Joker, and Catwoman. That leave's Ares, Sinestro, Harley Quinn, Killer Frost, Black Adam, Solomon Grundy, and Doomsday.
Another easy way to complete this is to fight the AI in "Single Fight" on VERY EASY under the Single Player Menu. Choose Batman for every match, and cycle between the 12 villains as your opponent. The villains are all located on the right side of the Character Select Menu.