Describe some of the military accomplishments of the Assyrians.

The Assyrians, like the Spartans of ancient Greece, were a warrior society. Every male member of that society was expected to fight as and when required. And as the Assyrians eventually came to defend a rapidly expanding empire, this became ever more imperative.
It is therefore not surprising that, over the course of centuries, the Assyrian Empire achieved a formidable reputation as a military power, building in the process the largest empire in the ancient world until the time of Alexander the Great. The chief basis of their extraordinary might came from having an exceptionally strong, well-trained, disciplined standing army.
Initially, the Assyrians, like other armed forces in the ancient world, relied on conscripts to fight their battles. This was to enable crops to be harvested as the vast majority of part-time Assyrian soldiers were farmers who were needed to work the land. But under the military reforms of King Tiglath Pileser III all that changed. From now on, soldiers would be full-time professionals. This enabled the Assyrians to conduct warfare much more flexibly, as they were now able to take to the battlefield all year round, even later on in the year when the harvest was due.
The Assyrians were also notable innovators in the fields of military technology and tactics. A prime example of this can be seen in their use of siege warfare. Assyrians were not the first to use siege warfare tactics, but they perfected them almost to an art form. Siege towers, ramps and battering rams were just some of the highly advanced military innovations used by the Assyrians to carry out their equally innovative tactics.
The use of iron weaponry also changed the nature of warfare and contributed greatly to Assyrian success on the battlefield. Traditionally, most weapons were made of bronze; but iron was a much harder, more durable metal. It also had the advantage of being cheaper, and as the empire became increasingly over-stretched and difficult to manage, cost considerations grew in importance.
It must also frankly be acknowledged that the use of terror was a key factor in the Assyrians' military successes. They were utterly ruthless in this regard and gained a reputation for almost unimaginable savagery among their conquered subjects. The siege and subsequent destruction of Lachish in 701 BCE is a truly chilling illustration of the unrestrained bestiality shown by the Assyrians to anyone who dared stand in their way.
 
https://www.ancient.eu/Assyrian_Warfare/