Due to the nature of Nuzlockes et al., what rules are in play are always decided by the player. However, due to popular request we have a few details those might want to consider such a challenge in Reborn and aren't sure where to start.
 

Reborn includes some battles that are intended to be scripted losses, but can be beaten. You may or may not want to count team member losses from these fights, but we recommend not considering them a run loss regardless.

Reborn includes a high volume of static encounters and an increased shiny rate. Whereas traditional Nuzlockes allow any number of shinies and static encounters, a popular community rule is to, in addition to the single first wild encounter for each area, limit yourself to one static encounter and one shiny encounter per same area as well. 

In a game like Reborn the lines between each area can become rather blurred. Below is our suggestion on what would count as distinct areas. Please be advised that some place names may be considered spoilers.

Players can also use the "nuzlocke" password to enforce mon death in their own playthroughs. This places no limits on what Pokemon can be caught.