After some brutal tries and tests, i figured out what to do here. I used my iphone to "Allow" the two factor code, and then on the apple tv it asked me for the two factor code. I entered the two factor code, but it still did not take. On the next go around, it asked for my standard password on the next screen, and i used my regular itunes password and ALSO included the 6 digit authentication code into my password (no spaces or dashes) so when asked for my password i used ----> mypersonalpassword123456 (123456 is an example of the 6 digit code apple sent me on the two factor authentication.
So if served/asked:
1. email and itunes password should be entered as normal
2. "allow" the two factor authentication on your iphone or ipad.
3. If apple tv requests the two factor password, use the 6 digits here from your phone.
4. Apple will probably reject the 6 digit code.
5. enter email again for itunes when prompted.
6. in password box, again, i used ----> mypersonalpassword123456 (123456 is an example of the 6 digit code apple sent me on the two factor authentication.
Hope this helps.
I know for me I was about to go nuts trying to get this to work.
Cheers.