The higher perfection is the spiritual perfection, integral union with the Divine, identification with the Divine, freedom from all the limitations of the lower world. That is spiritual perfection, the perfection that comes from yoga — quite independent of the body and the physical world — which, in ancient times, meant first rejecting the body and the physical life so as to have a relation only with the higher world and finally with the Divine.
That is the higher perfection.
Ref: Questions and Answers 1957 – 1958