Erstwhile Independent Senate Candidate Herbert Hoffman has has not yet begun to fight, apparently. His lawyer is taking the first steps towards appealing his case to the Supreme Court. MPBN has the story, PolitickerME has more, and here's Hoffman's own release.
How likely is it that the Supreme Court will hear the case in time for the election? Not likely at all, according to Lyle Denniston, author of SCOTUSblog, who has covered the court for the past 50 years. He emailed this response:
The Supreme Court, as a general rule, has shown little interest in recent years in ballot access cases. Unless there is some special situation here, review would not be likely. Unless the would-be candidate files a request for an order to block the ruling and put him on the ballot, there is no chance the Court would act on the case. It is in summer recess now until late September, and will not take up new cases until then -- aside from any application for emergency access to the ballot.
From my understanding as a non-lawyer, Hoffman has only filed for a stay of the court's ruling, not an application for emergency access.