Is it possible to back-up a cartridge version of a 3DS game (or one sold in retail)?
From Nintendo's support page:
Obviously, this means that only downloaded E-Shop titles will be able to use the Backup functionality. If you bought your game through a retail store or bought a physical copy, you will be unable to back up your saves.
You can only back up your save via the save data transfer tool. Meaning you need a physical copy of a game and digital one (Preferably not used) after you send your data to the digital (It cant be returned to the cartridge) you can back up your game if it has the feature. I am sure 95% of games have it.