LogFAQs > #963915284

Also, I took on the challenge of beating Dark Souls II without using bonfires, and I did it. Dying does not count against the challenge.

The game does have an actual reward for pulling it off, and that's why I tried it. The game awards the player the accessory:

Illusionary Ring of the Exalted

It's kind of a weird ring, as it makes your main character's equipped weapon invisible, and it seems to adjust the weapon's sound effects to be less pronounced.

There is a second type of this ring, but that one is far tougher to get. The player can access bonfires, but dying once counts as failing the challenge.