Lies upon lies were written by an Instagrammer with an extremely big ego, claiming to have held 2 PhDs by the age of 19 and subsequently 4 by the age of 31. Also, touting an IQ of 170+ and deeming everyone around him to be as dumb as apes. I have screenshots of all of this and his Instagram account username. These are not direct messages, they were written on a public post. If I post screenshots of these comments on an academia subreddit or any other platform in general, is this against the law? Regardless of whether or not it is a valuable use of my time. Thanks!
In general, this is against the law
Assuming that the user’s posts are protected by copyright (which if they are, as you suspect, works of fiction they almost certainly are) then you do not have permission from them (the copyright owner) or Instagram (a copyright licensee) to reproduce them. Instagram’s terms say:
You can't post someone else’s private or confidential information without permission or do anything that violates someone else's rights, including intellectual property rights (e.g., copyright infringement, trademark infringement, counterfeit, or pirated goods).
You can reproduce them under the fair use/ dealing exemption if applicable.
Of course, it seems that you will be implying that the statements they made are untrue. That might be the case, indeed, it probably is. But if they are true then you will be defaming the person by calling them a liar.