I don't know much about Instagram, but if they haven't left any contact information, you may be out of luck. Unless you can send them a private message within the site, but it looks like this might even be an abandoned account.
Another thing you could consider is contacting Instagram and asking them to grant you the name. If the account has been vacant long enough, they may be willing to shift it over to you.
But again, I don't know Instagram, so I have no idea what their policies are on this sort of thing. It's worth asking, but don't get your hopes up, because they don't have to do anything.