So the earliest account of the battle, given by Herodotus, does not go into much detail about the tactics used. He tells us that in the first engagement Cyrus followed the advice of one of his advisors, Croesus. They feigned a defeat and left an elaborate banquet for the Massagetae (Tomyris’ tribe) including a great deal of unmixed wine. The Massagetae, who did not drink alcohol, become intoxicated very quickly and are then killed or captured by Cyrus, including Tomyris’ son. He talks Cyrus into loosening his chains, and then commits suicide, making Tomyris swear revenge. Herodotus 1.214 then describes the second battle and Cyrus’ defeat:
“Such was the end of Spargapises. Tomyris, when Cyrus would not listen to her, collected all her power and joined battle with him. This fight I judge to have been the stubbornest of all fights that were ever fought by men that were not Greek; and indeed I have learnt that this was so. For first (it is said) they shot at each other from a distance with arrows; presently, their arrows being all shot away, they rushed upon each other and fought at grips with their spears and their daggers; and for a long time they battled foot to foot and neither would give ground; but at last the Massagetae had the mastery. There perished the greater part of the Persian army, and there fell Cyrus himself, having reigned thirty years in all save one. Tomyris filled a skin with human blood, and sought for Cyrus' body among the Persian dead; when she found it, she put his head into the skin, and spoke these words of insult to the dead man: "Though I live and conquer thee, thou hast undone me, overcoming my son by guile; but even as I threatened, so will I do, and give thee thy fill of blood." Many stories are related of Cyrus' death; this, that I have told, is the worthiest of credence.”
As you can see it sounds like an open field battle whereby the Massagetae seemingly got the upper hand, without much in the way of tactics.
Later sources though ascribe trickery on the part of Tomyris to the victory over Cyrus:
Orosius 2.7.4:
“She feigned anxiety and despair over the disaster that she had suffered and retreated gradually, drawing the overconfident enemy into ambush. By placing ambuscades among the mountains, she destroyed two hundred thousand Persians together with their king; beyond all else, her delight at this success was increased by the fact that not even one man survived to carry news of the disaster.”
Justin 1.8.9:
“But Tomyris, after losing so great an army, and, what she still more lamented, her only son, did not pour forth her sorrow for her loss in tears, but turned her thoughts to the solace of revenge, and entrapped her enemies, exulting in their recent victory, by a deception and stratagem similar to their own. For, counterfeiting timidity on account of the damage which she had received, and taking to flight, she allured Cyrus into a narrow defile, where, placing an ambush on the hills, she slew two hundred thousand of the Persians with their king himself; a triumph in which this also was remarkable, that not a man to tell of such a massacre survived.”
So it seems the key strategem was to lure Cyrus into unfamiliar terrain and launch an ambush amongst the mountainous routes. From a military standpoint the tactic makes sense, as the Massagetae were a nomadic people and so hit-and-run tactics were going to be far more effective against a standard ancient force such as would have been used as Cyrus. The Scythians used similar tactics against Darius I a few decades later.
The strategy described by Ororius and Justin makes more military sense, but Herodotus was writing only around a century after whereas Orosius was writing in the 4th/5th centuries AD and Justin approximately in the 2nd century AD. This is centuries after the account of Herodotus and it is likely that the cultural shifts since the days of Herodotus made the common story more into a tale of “womanly” trickery, whereas Herodotus presents more of a straight forward and noble queen, whereas it is Cyrus’ deceit that is more noteworthy. Furthermore Xenophon says that Cyrus died peacefully, attested by the fact that his tomb can still be visited in Pasargadae which presumably suggests the story of a complete massacre of the Persian forces is exaggerated.