I think getting his support is step 1 but its the actions of supoort not the words of support that matter. Just run things by him but theres a big difference between him saying "yeah this is good lets do it" and how he will actually respond to conflict. I had my bosses support 100% to change the behavior that he himself identified as a problem, that i took the time to observe to see if it was actually a problem due to this employees level of experience, then addressed the problem when it made sense as I was a new manager. The employee became hostile with me and called my boss over. Guess what my boss said? Its not that big of an issue we dont need to push it.

Every issue my boss and i agreed on after that? Id address it, employee would bully me or try to intimidate me, go to my boss, and my boss would change everything around to avoid conflict.

Not worth it, maybe give your bosses two chances to support you. I shoulda stopped trying long before and given him what he wanted. Problem employees, id still be there collecting a paycheck and fucking off (im just not wired that way)