How to remove your Nintendo eShop account
This applies to the eShop on your mobile device. Follow the steps named in the link.
Direct removal link: https://www.nintendo.com/consumer/systems/3ds/en_la/ht_apps.jsp?menu=nintendo%20eshop&submenu=ctr-ht-apps-eshop-remove-account
Helpful Trick: Removing online data
Publicly visible text/images often aren’t properly removed even when you succeed in removing an account. Try editing or removing them manually before removing the account itself. If you’re unsure what happens to your tracks: this can be found mostly in the Terms of Service/Privacy Policy; otherwise you can always contact Nintendo eShop and ask personally. By the way, removal requests don’t necessarily mean your data will actually be removed (e.g. due to legal obligations).
Helpful Trick: Remove third-party logins
If you signed up for Nintendo eShop using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Nintendo eShop. Click here to find out how.