Plot hole: The side mission "Fragile Alliance" has Batman helping Bane destroying containers full of Titan. After destroying the containers and returning to Bane, a small fight ensues followed by a cut scene of Batman trapping Bane. Bane has the drug Venom visibly going through his body the whole time so he could easily break out, but remains trapped through the rest of the game.
Batman: It was all a lie. There's nothing wrong with you.
Joker: Nice of you to say. But you of all people should know there's plenty wrong with me.
Trivia: Just before Protocol 10 starts, you end up in a giant fight with Joker and a good number of his goons. If you activate Detective Vision during this fight, you'll see that Joker doesn't have a skeleton. This is also true when he's holding Talia hostage in front of the move theater. This offers a hint to how the plot plays out.
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Answer: Batman later in the game discovers that Hugo Strange has been supplying everybody with weapons, so he would have given Two-Face the vat of acid.