If you’re on a Mac, use the shareware Print2Pict driver and print to file. Then you can open and select and copy out all the text, paste it into another application, and fill it out.
Try clicking on the outlined “T” at the bottom of the left-hand toolbar. You might have some luck there, unless the PDF has been password-protected for editing.
Adobe will tell you the security settings on the file. All you have to do is ask nicely.
If that doesn’t work, go to File --> Document Securty --> Display Settings. Check out the Form Field Fill In and Signing. If that’s allowed, you’ll need to click in the field in order to complete it.