I remember hearing of a tale, a myth perhaps, of these men that would focus on building their bodies and minds to peak performance. Does anyone here know the name of which they called themselves?
It's rather vague, so difficult to pin down what you're thinking of. Certainly there doesn't seem to be any example of what you're talking about in the body of stories that most people think of when they say "Greek mythology"; but I wonder if you might be thinking of Plato's account of the ideal guardians of the state in the Republic, books 5 to 7/ In his picture of utopia, the state is ruled by a class of ideal philosopher rulers. Could that be it?