I never understood this... Poison ivy isn't a misunderstood anti-hero, she's a villain. She's not a villain because she wants to save the world from pollution or climate change.
She's a villain because she's a mass-murderer and terrorist.
Also, Batman isn't opposed to her environmentalism, and a ton of his rogues' gallery are rich assholes. A situation like this would be likely to end in Batman stopping Poison Ivy and sending her to Arkham, but also stopping the billionaire's plans through destroying his project, exposing his plans, finding a reason to send him to jail, etc. It very much might involve kicking the shit out of a billionaire. More or less radical depending on who's writing that story.
And really, not to be a wet blanket, but Batman's been written by tons of people over nearly a century. Depictions of him and his surrounding characters are going to vary. Poison Ivy tends to be more of an antihero nowadays as her cause has only gotten more sympathetic.