Nintendo used to work with 2nd parties. A 2nd party developer is one developing a title exclusively for the publisher in thsi case Nintendo. Leftfield, Silicon Knights, N-Space, Factor 5 and Retro were all 2nd party developers. N-Space (Geist) still is. Retro (Metroid Prime) is now owned by Nintendo. Leftfield, Factor 5, and Silicon Knights no longer work with Nintendo at all. Meanwhile Kuju (Battalion Wars) is a 3rd party developer as was Capcom when they did a few GCN games.
There is no procedure for becoming a 2nd party develoer. As a former employee at Retro Studios, Jeff Spangenberg made a deal with NIntendo to be a 2nd party developer ata time (late 90s) when Nintendo was more willing to do that. Jeff also had a proven track record. he'd founded Sunsoft in the NES/SNES days, and then Iguana Studios/Acclaim Austin (Turok/NFL QBack Club). He knew people at NOA personally and did lots of networking. He didn't apply, he just went to them and said, I'm setting upa new studio give me money, at a point in time when they would.
So, if you want to be a Nintendo 2nd party, show a proven track record of AAA hit games for a few years as a 3rd party developer. Develop extensive personal contacts in NOA & NCL. And have impressive next gen tech. Or just give up. Or hope you get lucky and build contacts and a portfolio slowly.