There is no in-game "delete save" option. FFTA (GBA, played on DS via backward compatibility) writes a single save file to the cartridge's flash memory (or DS slot-1 save area for GBA carts).
Just start a New Game + or buy a $5 used cart. Formatting risks bricking the cartridge and loses the game itself.
Note: If playing the DS sequel FFTA2: Grimoire of the Rift, it uses standard DS save files deletable via System Settings → Data Management.