We know basically nothing about her early life. At some point she married King Eudamidas I by whom she had two children: Archidamos IV and Agesistrata. Her daughter went on to marry her own nephew, Eudamidas II, and had a son by him, Agis IV.
In 272 BCE, when Archidamia was already middle-aged, that Pyrrhus besieged Sparta. The Spartan council of elders, knowing that with most of their armies fighting in Crete, worried about the survival of the city. They debated sending the city’s women to Crete. Archidamia would have none of this. She came before them holding a sword and berated them for thinking that Spartan women would wish to survive the fall of their city. The women stayed. They helped dig a defensive trench* and, once battle was joined, brought the fighters food, water, and weapons as needed and helped bring the wounded from the battlefield. Pyrrhus and his army were soon forced to flee.
In her old age, Archidamia supported the attempts of her (great-)grandson Agis IV to reform Sparta according to the laws laid out by Lycurgus, taking it back to the austere values it had held so dear. As the two richest people in Sparta** she and Agesistrata donated much of their wealth to a common pool for redistribution. The exact nature of her support beyond this is unknown, but it must have been substantial. When Agis was murdered by his enemies, they found her enough of a threat to kill her immediately afterwards, despite her age.
*And by “helped” I mean dug a third of it themselves.
**Not just women, people.
Plutarch, Life of Pyrrhus 27, 29 - Lacus Curtius
Plutarch, Life of Agis 4, 7-9, 13, 16-20 - Lacus Curtius
Pomeroy, Sarah B. Spartan Women. New York: Oxford University Press, 2002.
Hodkinson, Stephen. "Land Tenure and Inheritance in Classical Sparta." The Classical Quarterly 36.2 (1986): 378-406.
Arachidamia - Wikipedia
Archidamia - Perseus (This is actually a modern poem to her, but I thought it was cool.)