Kaivalya, or isolation of the self, is attained according to Patanjali's Yoga Sutras when the illumination of the purusha (consciousness) and the chitta (mind) are equally purified and cleansed. The document discusses Patanjali's Yoga Sutra on attaining kaivalya or isolation according to the Vibhuti Pada section, stating that it is achieved when the illumination of the purusha and chitta are equally purified.