Completing this task took several steps because I had to interact with the file save applet. I find the save file applet is useful cumbersome and would prefer to use a simplified downloader like the one Firefox offers.
Path: Email Subject → 1st <no name> → 1st <no name> → 3rd <no name> → 1st <no name> → Panel containing HTML → 2nd <no name> → 1st <no name> → 1st <no name> → 1st <no name> → Save → [Take Action] → Select folder to save all attachments → 1st <no name> → 1st <no name> → 1st <no name> → 1st <no name> → 3rd <no name> → 2nd <no name> → 1st <no name> → 1st <no name> → Files → 3rd <no name> → Documents → Take Action → Select folder to save all attachments → 2nd <no name> → Save → [Take Action]