Then the Mexican government needs to "sack up" and use the drug cartels tactics against them. Leave "cartel employee" dead bodies as a warning and be even nastier than their current strategy.
Don't just arrest - shoot these leaders, their accomplices, and their relatives. Put it on National TV to show your opponents that you "mean business". Collateral damage be dammed!
Firebomb & destroy cartel compounds from the sky, if needed. For example, spray Agent Orange or Nuke a town to show - that you plan on winning. Even go as far as attacking the source, even another nation. Kill all prison & jail inmates to prevent cartel "ranks swelling".
It doesn't matter how you win - as long as you win. But, I am the only one who has the "balls" to use any means necessary to "get the job done".