Five years as empress regnant; nearly a quarter of a century as effective ruler of the state. She pretty much ran everything from 780 onwards; only in 797 did she eliminate her son and become sole ruler. The 797-802 dating is nothing more than a chronological convenience. I have to say, though, Tamar and Berengaria are definitely more obscure than Eirene is.
Her sheer political achievement in becoming the ruler of the Byzantine state was remarkable by itself. She was not the scion of an ancient and respected dynasty who just happened to be female; she was the parvenu widow of an emperor who was himself not particularly well loved in his own lifetime. The Roman imperator was defined by his ability to lead troops into battle from the very start, and that symbology had stayed with the office through the intervening centuries. I do mean his, because women certainly were not remotely close to being permitted to do anything of the sort. That a woman could therefore hold an office whose primary function she could not, by virtue of period gender roles, accomplish, was nothing short of astonishing. To hold the title of Byzantine Emperor was not a bog-standard feudal matter like in the Georgian monarchy or Castilian monarchy, and certainly nothing like the Romanov state of the eighteenth century. Only Wu ever did something so similar in its sheer improbability.
Among her first actions were to reverse the well-entrenched religious, military, and political supporters of the old Syrian dynasty to destroy the lunacy of iconoclasm; that she succeeded in this ought to place her among the greatest political geniuses of all time. (Not to mention its ultimate - positive - influence on Byzantine internal history. Iconoclasm was revived briefly by a few emperors after Eirene's death, but it never gained the sort of ascendancy that it had during the eighth century, and by the middle of the ninth century the whole schism was effectively over.) Her impact on religious life actually made a difference to pretty much everybody in the Byzantine Empire, regardless of wealth or social status, which is kind of a big deal. It's hard to imagine a random poor person in Tskhinvali caring much about anything Tamar and her court did.
And then came the bureaucratic reforms, and even the beginnings of a military revival. Eirene's bureaucracy was created virtually de novo to supply her with an alternative power base to the military; her creation of it and its enduring power actually meant that it's reasonable to describe later Byzantine monarchs as something other than military dictators for the following few centuries, before the bureaucracy was dismantled by the Komnenoi. And the military revival was huge. Revival in a long-term sense is rare in the history of premodern states, especially ones that suffered as mortal a blow as the Byzantine state did in the seventh century. That the Byzantines managed it, beginning with the framework that Eirene created, was extremely impressive. She even successfully defeated her own son, the actual Emperor, in a power struggle that by rights she should have lost before it even started.
This is all encomiastic, of course. She was cruel - that almost goes without saying. She was one of the worst mothers in the history of the world. She could at times be extremely petty, as the paranoid schemer types are wont to be. And even she couldn't keep up her brilliant run forever. She was not a nice human being. But she was a great monarch.