I've got this working and I thought I'd share what we did here. I know from searching this forum (and others, including Barracuda's) that some people have trouble with this, especially with the LDAP.
Here's the quick and dirty: to make Barracuda bind to Zimbra's LDAP server, you need the "ldap_nginx_password" from your "config.12345" file (the actual number will vary, of course). We found this in /opt/zimbra right after install.
Once you have that, enter the following on each Domain's LDAP setup page (Domain Manager, Users tab, LDAP tab):
Bind DN (username): uid=zimbra,cn=admins,cn=zimbra
Password: (the "ldap_nginx_password" from your config.12345 file)
We have the Barracuda 300 Spam firewall, version 5.1 firmware. We're using Zimbra 6.0.16 (as of this writing). If you have a different setup, use this as a guideline only.
Give Barracuda a good test email, save your changes, then click the Test LDAP button. It should work. If not, check the obvious: make the sure the port is opened on your Zimbra box, make sure typed in the password correctly, and so on.
Hope this helps someone. It's actually easy, and now our Barracuda is humming like a bird in front of Zimbra. We have a great mail server and a great spam filter, so I'm happy.