I have left a comment under a famous artist's post on Instagram. Someone else, whose account is private, keeps leaving insulting comments under my comment. Is there a way I can use to block that person from leaving his comments under my comment which I have left under the artist's post?
This is impossible. Based on the Instagram Help Center, people that you block can still see your likes and comments on posts that were shared by public accounts or accounts they follow.
What you can do is just reporting the users's comments and hope Instagram will restrict its comment in the future.