The irony of empire
Obviously, something prompted Polybius to write histories. Perhaps it is the fascinating development of the Roman Empire that brought him to the task; that is certainly one thing he comments about plenty. The irony of empires is simply that before the Roman Empire, the only empires which had existed were not nation states with official legal rights for citizens. There is dramatic irony too, because no one expect Rome to suddenly own the whole world, basically, but that's exactly what ended up happening.
The irony of legal balance
We take legal balance in the government for granted (during times of peace; perhaps sometimes more than others), but to Polybius, the government is absolutely fascinating. He observes the real drama of the Senate, the checks against the Emperor, the power of the citizens to get a law that actually helps them. These are all perfectly absurd decisions that were so essentially helpful that we still use the Romans as a reference for legal balance today.
The irony of invasion
There is an irony inherent to Polybius's telling of the Punic Wars. For one thing, Polybius records the Punic Wars from the point of view of a Roman citizen. As a military campaign, it costed Rome much. Many people died, and the economy was changed by the war, yet, the Punic Wars literally paved the way for Roman conquest. The full expansion of the Roman Empire depends on their being able to dominate Carthage. No one thought it would happen, and then suddenly, everyone is speaking Latin.
The irony of Hannibal
Hannibal is an ironic person to be mentioned in the story, because Hannibal was able to attack Rome from the North. Although they defeated him in the Second Punic war, Hannibal crossed the whole of Europe, through the Alps, to surprise attack the Romans. That is pretty ironic behavior, and Hannibal lost, but his story is still one of the greatest military dramas of the ancient world.
The irony of preservation
Although the document was not perfectly preserved, there is a case to be made that the most essential pure insights into the Roman world were preserved. That means we have permanent knowledge about the Romans, so ironically, Polybius was right to write his history, because it actually worked. He wrote the stories to preserve them, and it is a valuable insight into his world. It is ironic in the dramatic sense, because Polybius doesn't know that his efforts succeeded, but the reader obviously does know that.
