Acholius only appears four times in Historia Augusta and according Ronald Syme, is a hoax from imagination of Historia Augusta's author.
Historia Augusta said about Acholius this doubtfully career:
Acholius held the office of Magister Admissionum in the reign of Valerian (253—260 AD). One of his works was titled Acta, and contained an account of the history of Aurelian. It was in nine books at least. He also wrote a life of Alexander Severus.
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This article incorporates text from a publication now in the public domain: Smith, William, ed. (1870). "Acholius". Dictionary of Greek and Roman Biography and Mythology.