Usually when I need to do something like this I use python and BeautifulSoup4. You basically get the content of the web page and use bs4 to parse it and pull out the correct link. You will need to look at the source of the page to understand their page format.
If python requests isn't able to get the right data then you might need to use selenium to use a full web browser to render the page and run any Javascript that might populate the page. Then you send that page content to bs4.
Edit: I know someone posted a link to archive but I figured some instructions would also be useful.