The problem with a "solution" here is there's no way to know how the data is organized.
I'd say any relatively hack-free solution will involve a commercial backup application and a storage array of sufficient size to handle at least one full backup and some chain of incrementals.
Ideally the backup array would be of sufficient size and disk count that you could gain some small protection by creating independent disk groups each capable of each holding an independent file system for a full plus backup chains. I say this having supported large backup arrays where monolithic file systems were created only to corrupt, causing the entire backup to be useless. It doesn't protect against failures caused by faulty array controllers or enclosure failure, but nothing does but multiple complete arrays.
Decent commercial backup software will make the job simpler with compression, deduplication, intelligent incremental management, cataloging, etc.
CDW says $9,000 will get you a Netgear ReadyNAS with 12x4TB disk. In RAID-10, you'd have 24TB to work with. Combined with decent backup software this would result in a fairly painless way to backup that much data and manage it.
If you had nothing but time on your hands, you could roll your own solution with rsync, de-duped ZFS, etc but the hardware piece is still not cheap and rolling your own is nearly as expensive with a lot more headache.