Emily,

You will need to add the Attachment as a related item to the main object you are running the DDP from. For example, I have a DDP setup on my Opportunity Object and I want to capture the attachments on that opportunity as you've stated. 

First I create the DDP to run against the Opportunity. Then I setup a relationship where I have the Opportunity, I want the Attachment, and its relationship is the Parent ID of the related list (which is the Opportunity). 

This should be completely doable

Once I do that, in the field tagger, if I select the Attachment object, I can see a host of fields from the attachment list that I can grab and pull into my document.