When it comes to Pokémon Legends: Arceus (and most other Pokémon games), every Pokémon has unique stats, with the different stats being HP, Attack, Defense, Special Attack, Special Defense, and Speed. A Pokémon’s Nature will affect these stat pools in different ways, with the only unaffected stat being HP. 

If you’re looking for good Natures for a Pokémon, the best Natures will be ones that enhance the highest stats for that Pokémon. Much like previous Pokémon games, the Shinx-Luxray evolution line’s highest stat is always Attack, with Speed being Shinx/Luxio’s second-highest, while Luxray’s second-highest stat is Special Attack. Because of this, you will want to use Natures that will amplify Attack, Speed, or Special Attack, with Attack being the highest priority. The Natures that amplify the Attack stat are Lonely, Brave, Adamant, and Naughty. 

Lonely: raises Attack, lowers Defense. Since Defense is one of the line’s weakest stats, we can’t afford that drop in Defense.

Brave: raises Attack, lowers Speed, which makes it a viable Nature for a Shinx or Luxio to have, since a drop in Speed wouldn’t hurt their respective stat pools too negatively. However, Luxray’s Speed stat is significantly lower than that of its predecessors, so Brave may not be the best Nature for the whole line overall, unless you don’t plan on evolving your Shinx or Luxio.

Adamant: raises Attack, lowers Special Attack. This is a solid choice for any Pokémon from the entire line– Shinx and Luxio have Special Attack in the third highest slot for their stat pools, but upon evolving to Luxray, the Special Attack stat takes second stage over Speed.

Naughty: raises Attack, lowers Special Defense. This is not ideal for any of the Shinx-Luxray line, as Special Defense is the entire line’s lowest stat.

Since Shinx, Luxio, and Luxray all primarily use physical attacks, a dip in the Special Attack stat, one of their highest stats, will not hurt their competitive performance much. Therefore, out of the Attack-boosting natures, Adamant is the best choice.

However, since each of these Pokémon has such a high Attack stat already, you might want to boost Speed instead, in order to make sure that your Pokémon gets to attack higher up in the turn order. Looking back at that list, there are four Natures that boost Speed; Timid, Hasty, Jolly, and Naive.

Timid: raises Speed, lowers Attack. A viable choice, since the Attack stat is so high, but we want to keep that main stat as high as possible in order to effectively use these Pokémon in combat, making this one less than ideal.

Hasty: raises Speed, lowers Defense. Any loss in a defensive stat is a no-go for any Pokémon in this line– Defense and Special Defense are their lowest stats.

Jolly: raises Speed, lowers Special Attack. This is the best choice for a speed-based build; since Special Attack is relatively underutilized for how high it is in the stat pool. We can afford to take a hit in Special Attack.

Naive: raises Speed, lowers Special Defense. Again, any loss of defensive stats is a bad choice for this line.

This leaves us with two Natures being the best for the Shinx-Luxray line, Adamant and Jolly, with Adamant being the preferred choice for an Attack-heavy build, and Jolly being a good alternative for Speed-based builds.