Easiest way to get path of currently-opened file in Adobe Acrobat?
So here's an AppleScript that I pasted together with the help of some other answers and the AppleScript reference. This puts the URL of the frontmost Acrobat document to the clipboard, e.g:
file://localhost/Users/Your%20Username/Documents/Some%20Folder/Filename.pdf

 tell application "System Events"
        tell process "Acrobat"
            set thefile to value of attribute "AXDocument" of window 1
        end tell
    end tell
 set the clipboard to thefile