The only way to damage the big companies is with proportional fines.
You destroy the environment? 50% of your income gained in every country goes to those countries. I don't know why this isn't being advocated anywhere because measuring income is easy, the company has to do taxes and if they don't, 75% fine with the profits correctly calculated.
Hope they win. BP alone has $206.042B in revenue just within the last year. It's going to take a lot of lawsuits to even make a dent, but you gotta start somewhere.