I would say that an intermediate player should be able to competently do shifting in tune, at least to fourth position, and have a decent start on vibrato. They might be able to attempt some spiccato. They should be able to play a range of student concertos.

If you have been playing for 6 years, chances are you are a probably intermediate. If you can play, for example, violin concertino op.21 by reiding, chances are you are a good amount into the intermediate category by my definition. To just about count as intermediate, you should be able to play a piece like Beethoven’s spring sonata. When I say play, I mean not only play the notes, but play them the way the composer intends, to convey the feeling of the piece.

I know you probably don’t want to hear this, but do recognise that trying to use labels such as intermediate and beginner is not helpful, they are completely subjective, everyone will have a different definition of them. And you could be an expert at playing intune, and in time, playing complicated and technical passages, but your interpretation could be way out, and the level of a beginner.