If the server doesn't expose this list, you are out of luck: no way to explore the folder hierarchy of a server from outside if they don't want (otherwise, it would compromise security).
If it exposes the list,eg. with a classical folder listing (default if access isn't prevented by .htaccess or even a simple index.html file), indeed you have to parse the returned HTML page. Using a library is probably the cleanest solution, manual parsing is prone to errors on some cases.
If that's your site, you can also put a simple text file there, listing the image files. It might be easier to parse.