If you've already been convicted, it's going to be next to impossible to try to have it reduced now. If the case is somehow still pending, hire a locally experienced DUI attorney to deal with it, as it most likely would get dismissed. Best of luck.
If you have not been found guilty of this DUI, you should get an attorney right away and set the case for trial. It is very unlikely the State will be able to prove the case 23 years later. If you have been found guilty, then you should do the requirements.
I will second Mr. Palmer advise. It will be much cheaper for you to do what NV DMV wants, than to try and find out what happened in MN. If you were convicted of DUI 23 years ago they probably ordered you to do some of the things NV DMV is asking you to do now. If you have evidence of completion of the requirements, you can present them to NV DMV, if you don't, then you must do whatever they want you to do. The way they see it, driving is a privilege, not a right. Therefore, you have to jump through all the hoops they want you to jump through.