Are there any accounts of the Persian Empire that are not Persian or Greek? Are there Egyptian or Indian sources?
Other than the Greek and Persian sources, I think the only decent account of the Achaemenid Persians would be in the bible. However, it might be worth checking out "The Persian Empire: A Corpus of Sources from the Achaemenid Period, Vol. 1" by Amélie Kuhrt which would almost certainly answer your question.