Saphira is pretty durable, she can breath fire for about 1-2 minutes at a time, her scales act like armor, deflecting normal speed arrows (though never the rail gun arrows of doom as you describe Link's arrows to be). Her teeth and claws are the size of swords, and they tear through armor like tissue paper. She was able to shake off a blow from Shruikan, Galbatorix's dragon who was nearly the size of a small mountain, and then came back, pinned Shruikan (with the help of Murtagh's dragon) and held him down long enough for Arya to kill him with a spear through the eye.
So Saphira is pretty strong and durable.