As a historian, I think we could focus primarily on disrupting the cartels' supply of contraband and means of production, while hopefully not being drawn into a guerilla war. Take some of their military and personnel assets off the board, as well.
My biggest fear would be how dangerous the cartels would be to us domestically. I have seen experts talk about two really bad scenarios if we were to go to war with cartels:
1) Cartels deliberately poison the drug supply (even more than it already is) and overloading the US healthcare system.
2) Cartel members and affiliates in every city in America who are well armed and have murderous intentions being given orders to create mass casualties