He doesn't have to win in court. The deal with the electors is that it's purely a political battle now. It would be nice if the courts sided with Trump but Pence (Or Grassley, if the rumours about Pence are true) doesn't actually have to listen to what they say. Most courts, and even the Supreme Court, don't have standing to prevent Pence or whoever from counting these alternative Republican electors instead of the ones certified by the governors.
It's going to be an ugly process and, to be honest, by the end of it we may not be talking about President Trump or President Biden but Acting President Pelosi (if she is re-elected as Speaker).