What Dr. Venture Actually Did to the Monarch to Make them enemies is...
...nothing!
A lot of people, including characters in the show, have asked what Dr. Venture did to the Monarch to make them enemies. Well, this is actually explicitly addressed in a sneaky way early into the series. I noticed this years ago and posted it then, but people never really seemed to catch it.
If you pay attention to the episode where the Monarch tries to win back Dr. Girlfriend in season 2 (I think it might be called Hate Floats), there's a scene where they are arguing over the radio and the Henchmen can hear them. The Henchmen are talking over the conversation, but if you listen really carefully you can hear Dr. Girlfriend say something like, "And besides, you waste all your time and talents arching a loser scientist who never even did anything to you in the first place!"
Since they know each other so well, and have been dating for years, surely they discussed Venture at length. So she knows the Monarch started arching him for no real reason. It was likely just arbitrary, so for something utterly miniscule, like making fun of his butterfly poetry in college.