The greeks and later the roman classified history as a succession of Empire witch had "world domination". Some lists of those empire contradict with each other but here is the most generic list taken from Velleius Paterculus, copiing an otherwise unknown author named Aemilius Sura.

He lists:

1. The Assyrians

2. The Medes (persians)

3. The Macedonians (including the successor states)

4. The Romans (after the victories over the Macedonian and Seleucid kingdoms)

Now to return to your question, this idea of the assyrian domination, dating from an era when greek history didn't existed left traces on the stories about Semiramis, legendary queen of Assyria. She supposedly conquer Asia and was only stopped in India, an idea clearly modeled over the limits of the Persian Empire, dominant during the time of Herodotus.

Similarly the main figure for Persia was Cyrus, founder of the Persian Empire, victor over the Babylonian and the Lycian kingdom of Cresus, he was the hero of the Cyropaedia of Xenophon, a book on the eduction of Cyrus as a model of good upbringing. Even if it's not really an exact depiction of persian education it shows the power of the figure as an iconic example.

When Alexander conquered Persia, he knew very well about Cyrus and Semiramis and made his army pass trough the desert of Gedrosia supposedly because the two previous monarchs did it before him.

Besides the theory of the succession of Empire (witch influenced a lot the writing of the book of Daniel), there were other world conquerors: Herodotus says that the egyptian Thutmosis (that we can identify with Thutmosis III) conquered lands up to Scythia. Maybe an exageration (from his egyptian source?) based on the idea that the Persians failed mutiple times to conquer it. A last king worth mentionning is Nebuchadnezzar, the king of Babylon. I don't really know about his depiction in Herodotus but in Babylonia he was recalled as a great king, and as such was a model (or at least showed as one by the priest of Marduk, god of the city) for the persian and seleucid kings who controlled Babylonia. Those kings performed (in theory) each year a crowning ritual at the Temple of Marduk. This is capital because we know from Berossus, a babylonian astronomer at the seleucid court that he considered Nebuchadnezzar as a world conqueror. We also know from an "astronomical diary" (summary of the event of the years, mentionning the planets, some events, the price of wheat), that in 187BC Antiochus III, seleucid king just defeated by the Romans (see the transition between number 3 and 4 in the list) came to do the coronation ritual (named Akitu in akkadian), he took the robe of Nabuchadnezzar to show is legitimity as a Babylonian king.

Those elements shows how memory is transmit trough generation and sometimes, willinly repeat itself for self-legitimation of the rulers. As such some key figures foreign to the greeks entered and marked greek litterature. The integration of those lands in the greek world with the conquest of Alexander made those relations even more intricate. You can see that It focused on kings, it was not their history after all. Note that it changed a bit with Polybius when he wrote on Hannibal but his project was a universal history of the last 80 years so he had more accurate sources. I could have mentionned other Persian kings such as Darius or Cambyse but they were not really military legends as the main source is Herodotus and those events were quite recent and not really legendary.