Mapped Network Drives

Assume this server named as proxy_server. 

Double check that your NetBackup Client Service does not use "Local System" account to log in, just because this account cannot be used for the network authentication: use dedicated domain account for your NBU.
If you don't have such an account in your domain (yet), just create it for that purpose, add it to the Local Admin group and make sure that this account has at least read permissions at the file share. Change NetBackup Client Service logon credentials to that account/password.

Now go to the NetBackup and create a regular MS-Windows-NT policy, check box "Backup Network Drives", put your server in the client list and \\server\share\...whatever to the backup selection list.

Basically that's it.