Only looking at your example, it shows -A nc4,xml which would explain only downloading .xml files, there must not be any nc4 files at that link.
Anyway, here's what man wget says about -A:
Recursive Accept/Reject Options
-A acclist --accept acclist
-R rejlist --reject rejlist
Specify comma-separated lists of file name suffixes or patterns
to accept or reject. Note that if any of the wildcard
characters, *, ?, [ or ], appear in an element of acclist or
rejlist, it will be treated as a pattern, rather than a suffix.
In this case, you have to enclose the pattern into quotes to
prevent your shell from expanding it, like in -A "*.mp3" or -A
'*.mp3'.
So for only grb files, try using -A grb as in:
wget --load-cookies ~/.urs_cookies --save-cookies ~/.urs_cookies --keep-session-cookies -r -c -nH -nd -np -A nc4,xml "https://hydro1.gesdisc.eosdis.nasa.gov/data/NLDAS/NLDAS_FORA0125_M.002/1985/"
After Edits:
Username & Password should be fairly easy, try adding these:
--user=user
--password=password
Specify the username user and password password for both FTP
and HTTP file retrieval. These parameters can be overridden
using the --ftp-user and --ftp-password options for FTP
connections and the --http-user and --http-password options for
HTTP connections.
again from man wget. And read about the --save-cookies file and ``--read-cookies file` options in there, it may be tricky to get cookies saved from a web browser, if they don't work in wget.