The World Needs a HeroG 50

See the solution for Pandemic God. While not specifically targeted to this achievement, the method detailed there is basically your only shot. The only addition would be that if you cannot cure a disease within the first round (i.e. after one turn each by the Scientist and Researcher), quit and start a new game. If a disease can be easily eradicated, this will also benefit you (i.e. blue can be eradicated within 1 turn by moving to Washington or Montreal).