It's a problem that's hard stop, but Instagram is fighting back against online bullying.  On Thursday they introduced a new tool that blocks offensive comments and a filter that removes spam in comments.
Wanna use the new blocking tool?  Tap on menu on one of your photos and just scroll down to “Comments”.”  The turn on “Hide Offensive Comments.”  The tool will block offensive comments, like explicit sexual content or harassment, on both posts and live video. You’ll still be able to report, delete and turn off comments. By the way, the comments are hidden from everyone except the person who made the offensive comment so they can’t work around the technology.