Esther Chapter 9 is often cited as a Pinpointed Lunar Sabbath. This is because the Israelites rested on the 15th of the month of Adar, and this would place the Sabbath of the month on the 8th, 15th, 22nd and 29th.
This page presents the rationale for considering it as a Pinpointed Lunar Sabbath, and discusses several objections.
Esther Chapter 9 describes the victory of the Jews over their enemies on the thirteenth and fourteenth day of the month of Adar (the twelfth month). Verse eighteen documents that the Jews rested on the 15th of Adar. This proves that the Sabbath fell on the 15th, and that the other weekly Sabbaths were on the 8th, 22nd and 29th of the month.
The "rest" described in Esther 9 is not the same as a Sabbath. When YHVH rested after six days of creation, the verb used is "Shabath" (שַׁבָּת), Strongs Number H7673. This is the verb form of the noun "Sabbath".
In contrast, the verb used in Esther 9 to describe how they rested is "Nuah" (נוּחַ), Strong's Number H5117, meaning "to rest or pause". It is not the same thing as a Sabbath, and the author of Esther likely used this alternate word to describe the day since it was not a Sabbath that they were observing.
Additionally, we find in verses 16-18 that the Jews in the King's provinces rested on the fourteenth instead of the fifteenth:
But the other Jews that were in the king's provinces gathered themselves together, and stood for their lives, and had rest from their enemies, and slew of their foes seventy and five thousand, but they laid not their hands on the prey, On the thirteenth day of the month Adar; and on the fourteenth day of the same rested they, and made it a day of feasting and gladness. But the Jews that were at Shushan assembled together on the thirteenth day thereof, and on the fourteenth thereof; and on the fifteenth day of the same they rested, and made it a day of feasting and gladness. (Est 9:16-18)
This poses an additional problem because the definition of the weekly Sabbath is that it is a rest day following six working days. If the Jews living in the King's provinces rested on the 14th, then that would mean that the 15th could not have been a Sabbath because it was preceeded by only five working days and a day of rest.