Hey Paul,
There's not a super-easy way to do this, but there are a few custom (unsupported) apps that will make this easier.
The first I'll mention is the AttachmentGrid: Custom APP to display attachments with link for scoped user stories. It basically lists out all your stories and you can filter for what you want (although via a query) and it will display a link to your attachment to make downloading them easier.
If you really want to go all out though, there is Rally-Export-Attachments: Ruby script to export all attachments from a specified Rally Workspace for… . Basically a ruby script that will export all attachments. A bit harder, but maybe easier depending on your skillset!
I know neither of those are probably exactly what you're looking for, but hope it helps!