Batman (the comics, anyways) is full of villains like that. Mr. Freeze just wanted to save his wife and went off the deep end after people pulled the plug on her cryogenic stasis pod, killing her. Poison Ivy was a biologist who worked on saving the world from ecological collapse and came to the conclusion that humanity would never change in time to save itself, so the only way to save the world is through violence, which is why she usually targets companies polluting the environment and their owners. Cat Woman is often depicted as either a petty thief making big scores for the thrill of it, or Robin Hood, stealing from the rich and donating the money to cat shelters and stuff. Sure, there are plenty of more standard villains in Batman, but when done right, Batman is largely the story of a broken man trying to save other broken people and stop them from hurting themselves and others.

The most literal example of a villain trying to save the world I can think of is Ozynmandias in The Watchmen. The story revolves around a plot by Ozymandias to basically explode two nuclear bombs and make it seem like attacks by Dr Manhattan in order to stop the Cold War from going hot by uniting the Soviets and the US against him. The comic is a total deconstruction of the genre, but it’s definitely the most outright “the villain saves the world through mass murder” story you can find.