There is no attested word "achaara" referring to a pickle in any Sanskrit dictionary I know of (I just checked several). The standard Sanskrit words for pickle have very clear analyses, i.e. avaleha ("licked down"). A similar analysis of "achaara" in Sanskrit would lead to a nonsense meaning of "not-moving".
Whereas, there is a clearly related Persian word "achaar" for a similarly preserved food, which apparently doesn't appear in any Indian texts prior to Mughal rule of South Asia.
Even if there were a shared Avestan/Sanskrit antecedent, many words that share a common ancestor in those languages got re-borrowed in their Persian form into Hindi during Mughal rule.
For example, the common Hindi word "garam", meaning hot, is a direct borrowing from Persian "garm". It replaced a related word for hot/heat from Sanskrit: "gharma" (the loss of original aspiration on the "g" is a feature of Persian). Both words share the same origin, but the Persian version is the one used across South Asia today.
Similarly, Hindi "chaador" meaning "blanket", is a Persian borrowing that also has a Sanskrit cognate "chhaadana" meaning "cover".