Melanie Rosenberg
You should be able to go to the item page, find the layer in question that contains the attachments, then click the small arrow next to the layer name to export to a file geodatabase. The file geodatabase should get created as a file item in My Content, which you can then download.
If you are having problems exporting, there may be a problem that is specific to your hosted layer. In this case, I recommend calling Esri Support so they can troubleshoot the problem.
Thanks,
Mike