!!! Tapas doesn't let you have more than 2000 characters in a description, so if you're curious to know how exactly nuzlocke rules a bit different to the normal rules, please check the description of this cover link - https://www.deviantart.com/pigeonperson/art/Silence-Pokemon-Platinum-Nuzlocke-Comic-Cover-855414698 !!!
You can however find the main rules down below here.

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RULES

You can only capture the first encounter in every area.

Dupes Clause is on - if you encounter a pokemon you’ve already caught, you may flee and catch the next one.

Once a pokemon dies, Dupes Clause for the species goes off, meaning if you encounter a pokemon of the same species/evolution line as your first encounter, you have to catch it.

If the first encounter is a double battle, you can choose which you’d like to catch.

If you happen to encounter a shiny pokemon that isn’t your first encounter/is Dupes Clause, you are still allowed to catch it and use it.

Gift pokemon are allowed to be used.

Starter/Egg pokemon acquired in a certain area do not count as that area’s capture.

Any pokemon that faints is immediately considered dead, and must be permanently put in the Storage System or released.

You must give a name to every captured pokemon in order to grow a stronger attachment towards them.

The nuzlocke begins once you acquire pokeballs from either the store/Lucas.