If your files & attachments are related to the Case Email then you can download them from Email Message.
Follow the below steps to Downalof files & attachments from "Email Message" in bulk.
1. Open the "Mass File Download" Tab and Click on "Related Files & Attachments"
2. Now select the "Email Message" form Select Object drop-down
3. Select Advanced Search (SOQL) search mode and hit the Search Button, As shown in the below Image.
4. Now hit the Download Files & Attachments button and download up to 2000 files at one time and then another 2000 files and so on