There are multiple steps to be done for getting MySQL to run under medium trust.
1. Recompile the ADO.NET data driver. Cause the first error you will get when using any MySQL.Data.Dll function is
Additional information: That assembly does not allow partially trusted callers
This procedure is described in these articles on Medium trust MySQL ADO.NET driver - also running [...]
Having your ASP.NET 2.0 application working under Medium trust has gotten more and more important – since many webhosts only run 2.0 under medium trust.
As a developer you can set trust level for your specific site you are testing at the moment by changing web.config
<trust level="Medium"/>
</system.web>
</configuration>