What a fascinating question! I think one simple way would be to show people with mental health problems being successful, in positive roles etc., and encouraging famous role models to be very open about their mental health difficulties as part of a campaign. The other possibility is to show postive outcomes of spending time talking aout mental health problems - not just for thoese with such problems, but for others too in terms of learning and being able to apply that knowledge in everyday life. Hope that helps!
My question is why you think that this will work. Classical conditioning theory ignores the social embeddedness of people. It's about individual manipulation not social change, control not consensus.
There is a myth that stigma is a set of mistaken beliefs about a group of people. Stigma runs deeper than that. It is a form of rationing social resources. So stigma is discrimination.
You need to look at evidence from successful campaigns. There's a lot of interesting literature.
Have a look at this review for a start: https://www.nap.edu/read/23442/chapter/6
Also useful :Article Interventions to Reduce Mental Health Stigma and Discrimination