Something I'd find a way to work in is a situation in which you've had to argue for something (or do something) you didn't necessarily agree with. As a clerk/intern, you'll be called upon to draft opinions/memoranda that support a position the judge wants to take that you might disagree with.

I'd also work in that you value privacy and confidentiality, because chambers tends to be very private and insular, and your judge will need to trust you a lot.

Finally, judicial internships and clerkships are very much on the academic side of things, so I'd make clear that you enjoy researching the law and reading and writing about the law and that the reason you want to do this is to be a part of a system that shapes the law.