I solved this :)
This is what is needed:
Edit the SlideShowPlugin.php file, found in the "classes" directory of this plugin.
Find this string by searching for the word "admin":
admin_url('admin-ajax.php?action=slideshow_jquery_image_gallery_load_stylesheet&style=' . $styleName),
replace with this:
'/home/username/public_html/wp-admin/admin-ajax.php?action=slideshow_jquery_image_gallery_load_stylesheet&style=' . $styleName,
where /home/username/public_html/wp-admin/ is the full path, on YOUR SERVER, to your wp-admin folder. Basically, we are replacing
i.e. place it ALL inside the single quote, and remove the parenthesis
Save the newly edited file, and try to visit your front-end again...it should no longer request the login. This is because PHP is an internal process, so it doesn't require validation via htpassword, provided it uses server paths, as opposed to WP hooks or publically-accessible urls.
Hope this helps :)