There has never been a book about Artemisia I of Halicarnassus, not even a full academic article. I wrote some academic articles about the Persian Stoa that the Spartans built with a depiction of her many moons ago, in the context of research on Caryatids. The research on her so far has been of that fragmentary nature, which is surprising considering she was such an important military figure. The fact that she was both a woman and the best documented Persian leader at Salamis makes the vacuum even more striking.
More recently I've been blogging about Artemisia, and trying to write a book about her role in the Battle of Salamis: Artemisia is the main subject, with Themistocles and Xerxes as supporting characters, and Herodotus as the narrator.
Recently I found out that the current plan for the sequel to 300 is a female figure at the battle of Salamis - the director Zack Snyder dropped some heavy hints about the material Frank Miller is working on here. (The last plan they announced seems to have been for some sort of a prequel, and hopefully they will their eye onto another battle soon and forget Artemisia.)