I see 3rd Party developers split into 3 groups for Nintendo:
Group 1:
The low hanging fruit for Nintendo are definitely the Japanese 3rd party developers that are currently supporting the 3DS. Nintendo already has an active relationship with these developers and they should definitely try to secure their support on the NX (especially if the NX is going to be a unified console-handheld concept). Square Enix, Capcom, Atlus, Platinum, etc... are essential for the NX. They should try to get as many Final Fantasy, Monster Hunter, and Etrian Odyssey games lined up as they possibly can before the console launches. We also know that Nintendo fans will buy these games because Nintendo fans are the ones who are currently buying them on the 3DS.
Group 2:
The next group Nintendo should target should be western developers that Nintendo has past relationships with but have lost during the Wii U's life. This includes companies like UbiSoft, EA Sports, and Activision. I think if the outlook and hype surrounding the NX starts to look good as we approach launch, it will be really easy to get these developers back. If the NX sells well (ie. at least 30 million with a decent market share in the west) then these developers will probably be mainstays on Nintendo consoles again without too much effort from Nintendo. Nintendo fans will also likely buy these games on mass because a lot of these titles have a long history on Nintendo platforms prior to the Wii U era.
Group 3:
The last group are the western third party developers that don't have a strong past relationship with Nintendo: Bungie, Naughty Dog, Rockstar. These developers won't be easy to get on a Nintendo console because I don't think they even really supported Nintendo during the lucrative Wii era. I am also not sure if Nintendo fans would buy enough of these games for it to be profitable (even with a large install base). If I was Nintendo, I probably wouldn't worry much about securing the support of this group.