This is the easiest way for anyone who lives outside the US to get videos from Nintendo Video.
Just change the Primary DNS on your 3DS to 184.22.4.38 and the Secondary DNS to 184.22.4.37. And thats it!
This also works for Japanese 3DS systems.

 

[rg]

Is there a way like that if you have a European 3DS and outside of Europe (UK specifically)? Because none of the other methods worked for me.

Try using Google DNS servers maybe?

8.8.8.8 is the address
8.8.4.4

I'm not sure if these are outside US but are worth a try..

 

[fandy]

it's all not working
I'm from Indonesia, my 3ds region lock is U.A.E and i use hotspot wifi from my android phone. What the problem? please, help me..

 

[psynumb]

Hey! Thank you for posting this solution. Unfortunately, it didn't work for me though. For some reason I can't get connected to the internet (the connection test fails) as soon as I change the DNS addresses. Can you think of a reason why it's not working? Thanks in advance.
Oh! And I live in Qatar and own a US 3DS, if this helps.

 

[ultranoid]

Did not work for me as well. I tried pinging the servers and there is no response. Those DNS servers are apparently dead.

 

[Duo8]

Guess we need a new dns. Or use that proxy method.

 

[ov3rkill]

Yeah, this dns doesn't work anymore. Hopefully, we'll get a new DNS.