He did not, nor did Aratus of Sicyon, and though Galba and Otho are paired thematically, they aren't in the parallel format.

This is because none of them are actually from Parallel Lives, officially Lives of the Noble Greeks and Romans. The "Parallel" in Parallel Lives refers to the comparison of notable Greek figures to notable Roman figures, but that was not Plutarch's only biographical work. Unfortunately, most of his other biographies, literally Bioi (Βίοι) or "Lives," were lost. He did a series of Lives on the Roman emperors from Augustus to Vitellius, of which only Galba and Otho survive intact. Extended fragments from the Life of Tiberius and Life of Nero are quoted elsewhere, but most of the compilation is only known from passing references.

Plutarch also wrote standalone Lives on several figures. Artaxerxes and Aratus are the only ones that survive, but ancient and medieval lists of Plutarch's works include others, like Heracles, Hesiod, Pindar, and Phillip II. Even one set of parallels was lost entirely, Epaminodas and one of the Scipios were originally paired together.

Because of the similar formats and content, the four surviving standalone Lives are usually lumped in and published alongside Parallel Lives, sometimes just called Lives for that reason.

The Life of Artaxerxes is unique for another reason. It is the only one of Plutarch's many biographies written about a "barbarian" (ie not a Greek or Roman). Artaxerxes could not fit into the schema of Parallel Lives because they explicitly compared Greek and Roman historical figures. Plutarch does not state why he chose Artaxerxes as a subject in the biography itself, but scholars have theories.

The prevailing theory put forward by Eran Almagor in Plutarch and the ‘Persica’ is that The Life of Artaxerxes was probably written during the preparations for Trajan's Parthian campaign. In that case, Plutarch was using the Achaemenid king as a way to draw an indirect parallel between ancient Persia and Rome, rather than Artaxerxes himself and another individual. Artaxerxes II would be an ideal choice for this goal. He was already the best documented Achaemenid king in the 2nd Century CE and was presented favorably by popular Greek contemoraroes like Ctesias (Artaxerxes' personal physician) and even Xenophon (who fought against Artaxerxes). Artaxerxes II was certainly one of the best known, and apparently one of the best liked, Persian figures among the Romans, and thus an ideal point of comparison.