This is an alternate method of doing a no death/no bonfire run and getting the illusory rings.
Original Guide : https://youtu.be/UE1OG7-RjwM
By obtaining the Santier's Spear early and getting it to +3 raw, you can do the entire no death no bonfire without managing durability. Details below.

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Music Used
The Sims Soundtrack - Buy Mode 2
Powerwolf - Coleus Sanctus
Cuphead OST - 06 Inkwell Isle One [Extended]
Kill Bill Ironside Siren Sound
Don't drop that Pump-a-Rum [Dark Souls 3] - YouTube
Beyblade song - Let's beyblade
Instrumental Core - Dance at the Moonlight

The Santier's Spear is a weapon obtained in Doors of Pharros by opening a Pharros lockstone contraption. The reason why this weapon is one of the top choices for a NDNB run is due to its "infinite" durability. Technically the weapon itself has 500 durability but after breaking it gains infinite durability and a unique moveset which is much more supirior to its unbroken state.
By doing the Fragrant Branch of Yore jump in Forest of Fallen Giants you can gain early access to Shaded Woods and to an extent, Doors of Pharros. There you can obtain the Raw Stone and the Santier's Spear.
Personally, I would recommend the Rapier over the Santier's Spear since it is much easier to make, and repair powders are pretty common in SotFS anyway. But if you want to avoid running pass and instead kill all enemies before proceeding, the Santier's Spear is going to be the top choice.