You're in luck. While there's only a few truly stand out books for Achaemenid political history, specific dives into culture are plentiful and run from scholarly but accessible to niche corners of academia.

For really any topic in Iranian history, especially ancient history, I always recommend starting with Encyclopaedia Iranica. It's a free online resource with scholarly write ups on hundreds of individual topics. It's internal search engine is imperfect and spellings aren't always consistent in Persian history, but if that fails and you search "[your topic] Iranica" in Google, it often finds what you're looking for.

The Persians by Maria Brosius is as good a print starting point as you're likely to get. It's largely focused on culture and spans the three major non-Greek periods of pre-Islamic Iran (Achaemenid, Parthian, and Sassanid), each with their own separate section.

Forgotten Empire : The World of Ancient Persia edited by John Curtis and Nigel Talis is a really excellent collection of essays from scholars working with the National Museum of Tehran, the British Museum, and the University of Chicago - three of the largest Achaemenid collections in the world. Each essay covers a different aspect of Achaemenid culture and society.

The World of Achaemenid Persia : History, Art and Society in Iran and the Ancient Near East edited by John Curtis and St John Simpson is very similar in scope and style to Forgotten Empire, but was specifically from a conference hosted by the British Museum and has a few different authors/topics and is a little newer.

The Culture and Social Institutions of Ancient Iran by Muhammad A. Dandamaev, Vladimir G. Lukonin hits the nail on the head as far as this topic is concerned. It's a bit older (originally published in Russian in 1989) but dedicated explicitly to an overview of Achaemenid culture and Soviet scholarship often has a few perspectives that haven't been fully incorporated into "Western" Achaemenid studies.

From Cyrus to Alexander: A History of the Persian Empire by Pierre Briant is the book on Achaemenid Persia and has been for about 20 years now. In over 1200 pages it covers just about everything in political history and culture from the Achaemenid period. It's also just unfortunately expensive so I never recommend it first.

There are also more specific niche books about single aspects of Achaemenid history.

King and Court in Ancient Persia 559 to 331 BCE by Lloyd Llewellyn-Jones is a great, readable examination of court life and lifestyle under the Achaemenids that makes use of all available sources to try and synthesize one consistent view of how the Achaemenids themselves lived.

The King and Kingship in Achaemenid Art : Essays on the Creation of an Iconography of Empire by Margaret Cool Root is older and harder to find, but laser focused on the presentation of kings both intentionally and unintentionally in Achaemenid art and the development of the distinctive Achaemenid Court Style from sites like Persepolis and Pasargadae.

Consumed Before the King by Wouter F.M. Henkelman is technically a paper submitted for a conference, but it's also 110 pages long and on his Academia account, so I'll include it. This one is fully down the academic side of things, but is also a really useful detailed account of court practices and logistics in the main royal court, a queen's independent court, and a satrap's subordinate court.

A History of Zoroastrianism Vol 2 by Mary Boyce is a thorough and detailed examination of religion in the Achaemenid period from one of the most impassioned academic authors I've ever encountered. The only real catch is that mainstream thinking on Achaemenid religion and Zoroastrian history has changed a lot since Boyce wrote much of this in the 70s. By and large it's still the best overview of the topic, but I do recommend something more up to date like relevant Encyclopaedia Iranica articles or Zoroastrianism: An Introduction by Jenny Rose for comparison.

Last but in no way least: Women in ancient Persia, 559-331 BC by Maria Brosius is the book to read for the subject in question. Unfortunately, it was one of the first full texts really examining Achaemenid women with all of the available sources and is extremely academic - down to large chunks of untranslated German. That said, there really is no better book to understand the role of women in the Achaemenid period.