Common law prohibits the use of evidence obtained illegally...but only if the person who obtained it illegally is a state actor, like the police. Evidence obtained illegally by vigilantes is generally admissible in a trial. Additionally, the state can be held liable for acts of torture performed by state actors.
But would Batman be considered a state actor? He operates mainly as a vigilante and does whatever he wants to do without a direct mandate from the state, but he works very closely with Commissioner Gordon, and the police can specifically summon him with the Bat Signal.
What do you think? Is Batman a state actor? Would any evidence that Batman illegally obtains be inadmissible in court? And could the Joker successfully sue the state when Batman roughs him up to get him to talk?
Is Batman a State Actor? | Law and the Multiverse