This word, here translated into the cognate acroamatics, comes from the ancient Greek ἀκροαματικὰς which literally translated means "things designed for hearing only" and refers to the lessons which Aristotle himself reserved for his closest disciples.
Similarly, epoptic is also a cognate, this from the ancient Greek word ἐποπτικὰς which literally means "highest mysteries" but refers to the teachings reserved for the ἐπόπτης, or "observer" who is an initiated member, often of a religious group.

Citation
Plutarch.Life of Alexander. VII. 5 Trans. Sean Rogers.