In English we make mention of the 'bible' or the good 'book' or the 'scriptures'. None of these words, in their origin, are exclusive to any one body of writing.
In certain circles 'bible' may refer to any central body of reference. Arthur Vogel's extensive production can be referred to as 'the organic chemist's bible'.
But within (let us say) Protestant circles there would be no doubt what was being referred to if one said 'bible' or 'scripture' or 'the good book' or even 'the book'. It would be that collection of writings which begins with Genesis and ends with Revelation.
Go back a hundred and fifty years and it would be very close to a certainty that one was talking about the Authorised Version of 1611 (1769).
Similarly, in the first century, at a time before any apostle had yet recorded anything written, to refer to graphe Strong 1124 (graphais, in Acts 18:24, being the dative plural and conveying a collection of what is written) it would be very obvious what was in view.
My 1,700 page Special American Edition of Liddel & Scott makes it clear that in profane Greek literature the term was not specific and, if anything, would principally refer to pencil work, artwork, or a painting as well as to a piece of writing or a legal document such as an indictment.
But within the writings of the apostles it is abundantly clear that they all use the term graphe to refer to holy scripture. That is to say, at the time of which Luke writes in Acts 18:24, the law and the prophets, as Jesus refers to the Hebrew scriptures, for example in Matthew 22:40.
Later, Peter uses the same term to refer to Paul's writings, 2 Peter 3:16, saying than many are wont to 'wrest' his words, making them seem to be other than they really are.
Paul, himself, then uses another word gramma Strong 1121 in referring to Timothy's upbringing, 2 Timothy 3:15, that, from a 'babe' he had known the 'sacred letters' perhaps conveying that Timothy had been taught to read, learning his letters out of the Hebrew bible, the word being more specifically focussed on what is actually, individually, on the page, rather than graphe which I would suggest refers to the pictorial shape (and therefore, by implication, the sense) of an entire word.
The word graphe occurs 51 times in the TR and in the KJV it is translated 'scripture' or 'scriptures' every single time (1). Glancing down the list it would appear to me that no other word, in context, would be suitable in any of this list.
As to Apollos, he was an eloquent man, mighty in the scriptures, this suggesting that, his eloquence being put first, the following mention of 'mightiness' - in respect of the graphe - would convey the meaning that his eloquence was centred on the Hebrew scripture and it was his spoken word, closely aligned with the holy writings, that was so powerful, so persuasive and so 'mighty'.
(1) Source is Robert Young's Analytical Concordance, 9th edition.