Frogborne is the only disease treated in the "Toad Hall" room. Toad Hall unlocks upon reaching Wave 7 of the Camouflage Falls hospital (the second hospital of the Close Encounters DLC) and is staffed by a nurse. Build the room and the achievement is yours after one successful cure. Several of the Camouflage Falls have goals to treat Frogborne, so this will happen naturally while progressing through the hospital.