It is possible, out of 22 official language in India Hindi is consider as top communication language.
But your writ will be reject and HC advise you to file in lower court ie. District or Session court.
I believe in higher courts only English is permitted. When a case goes on appeal from a lower court to the High court and when the judgment of the lower court was in a language other than English, a certified English translation has to be submitted with the appeal. To the best of my knowledge only High Courts and above have writ jurisdiction. One can fight one's own case without an advocate in any court.