The libertarian solution for protecting the environment is to privatize all land because private individuals are more concerned with keeping their property free from pollution than the state. And if someone is polluting their property they could bring charges against that individual and force him to pay for the cleanup.
But once you start getting into atmosphere and ocean things become less clear. First most people don’t normally apply property ownership rights to the atmosphere or ocean because people don’t live on the water or in the air like we do on land. A person could build a fence around a piece of land and claim it as his own. Or a person could claim ownership on the land underneath a lake or small body of water and claim the water above it as his property as well. Or even own a piece of beach front property and claim a piece of the ocean so many miles/kilometers/insert measure of distance out from it as an extension of his property as well.
But what about the vast stretches of unclaimed space that lie in the sky or the middle of the ocean? How could property rights be applied to these two things in a way that would proptect them from pollution in the same way that property rights on land do?
A person could sue a company or individual that was dumping toxic chemicals into the atmosphere or ocean for giving them some kind of illness or condition. But with global ocean and air currents it might be hard to prove that one specific company or individual was to blame.