A quick search on github returns this:
https://github.com/RipMeApp/ripme
Which seems to have support for downloading from instagram. Not sure if it does exactly what you want.
Instagram has an API, so in principle it should be possible to write exacly what you want as a small script. Like
https://github.com/LevPasha/Instagram-API-python
Should let you get access to the API from python, and save you some hassle if you have a python dev available. You might have to apply for a API key somehow from instagram, which should be straight forward if you have an instagram account, and I don't sadly.
You should also ask r/socialistprogrammers there there might be people who could whip something up.