How do you backup 100's of terabytes and live VM's?
Properly. As for "live" - that's why storage facilities generally have a snapshot capability. You accept that you have a gap between backups - how large it is depends on your backup frequency - but what you cannot afford is NOT having a proper backup. QED.
By the way, backup is what makes reliable storage so expensive. If it's cheap, it's an easy guess to assume that corners have been cut in the area of backup - be wary of that.