The standard Nuzlocke rules apply.
1) The first Pokemon encountered on each route/in each area are the only that can be captured. If the Pokemon flees, faints, or is unable to be captured no other encounter is allowed.
2) If a Pokemon faints it must be permanently boxed or released.
3) All Pokemon must be given a nickname.
4) In game trade Pokemon can't be used.
5) If the first Pokemon encountered is of the same species as an already captured Pokemon you are allowed another encounter.
A few additional rules for a Wedlocke include.
6) You must have 3 male and 3 female Pokemon in your party at all times (once a full team is assembled). Each male is paired with a female.
7) If one member of a pair is knocked out it can be replaced with another from your box if it is the same gender as the knocked out Pokemon.
8) Linked pairs can only swap between themselves during battle. If one faints the other fights until it dies to avenge it's link partner and cannot be swapped out.
9) If your party is not full or if your box has no suitable replacements you may encounter until the gender you need appears in new areas only.
10) Genderless Pokemon may be captured but cannot be used.
I did miss a few screenshots but I'll post what I have shortly.