Scenario of huge SQL Server Database backup
What you're looking to do is called a "piecemeal restore" and is pretty complicated. Here's a small pull quote from the MSDN article:


  Every piecemeal restore starts with an initial restore sequence called the partial-restore sequence. Minimally, the partial-restore sequence restores and recovers the primary filegroup and, under the simple recovery model, all read/write filegroups.


I'm assuming that your database is in simple recovery since you didn't mention any log backup schedule. So, if you ever need to restore your archive filegroup, you'll end up restoring the entire database.

If I were you, I'd try tuning your backup before going this route. For instance, try taking the mirroring out of the backup command note the time difference. You can always copy it to the secondary location after the full backup completes.

But, if you're looking to proceed with the piecemeal restore solution, the actual syntax isn't that bad:

restore database [yourDB]
filegroup = 'PRIMARY'
from disk = '\\path\\to\\full_backup.bak'
with partial, norecovery;

restore database [yourDB]
filegroup = 'PRIMARY'
from disk = '\\path\\to\\diff_backup.bak'
with partial, recovery;

restore database [yourDB]
filegroup = 'ArchiveFG'
from disk = '\\path\\to\\archive.bak'
with recovery;