Daniel prophecies Alexander the Great?

Hi all, new here. Had a visit from the Jehovah's Witnesses this morning. Good lads who were willing to discuss their beliefs and didn't try jamming a copy of The Watchtower in my hand at every opportunity. Much better than the Mormons who did the rounds a few weeks ago.

Anyway, the conversation turned to biblical prophecy and I was expecting to easily counter anything they threw out by pointing out ambiguities or obvious retro-fitting. But they came out with Daniel supposedly predicting Alexander the Great overthrowing the Medio-Persian empire. The 'prophecy' is notable in that it spells out what the symbols represent and I had to concede that it was superficially impressive.

It's the first time I've come across this particular passage. Does it have any obvious refutations? How does the sketpical community tackle this one?

No surprise that Daniel "predicts" Alexander the Great, given that the Book of Daniel was written around 100 years after Alexander died.

The Daniel Book (published by Watchtower Society)
Another impressive prophecy has to do with the succession of world powers after the fall of Babylon. If you have access to a Bible, open it to the book of Daniel and read the vision that Daniel was given in chapter 8. The angel who explained the meaning of that vision showed that Babylon would be succeeded by an empire ruled by the kings of Media and Persia. This kingdom in its turn would be overthrown by a conqueror from Greece. However, this Greek empire would soon be divided into four smaller empires.—Daniel 8:1-8, 20-22.
Was this parade of world powers fulfilled? It was indeed. Under King Cyrus the Great, Persia overthrew the Babylonian Empire in 539 BCE. This Persian Empire was eventually overtaken by Greek armies under the young Alexander the Great. However, when Alexander died, his empire was weakened, and eventually four of his generals became rulers in four divisions of it

others do not disagree with this. there were writings of jews welcoming Cyrus to Jerusalem as a savior and showing him the prophecy that was written about him. most christian apologists accept this as a prophecy of Alexander the great.

Much of what the JW's teach comes from other religions. Little of it can actually be attributed solely to the WTS, at least not in its beginnings anyhow. Today the confusing collaboration of dogmatic theology is much more identifiable to the JW's.