The description to earn this League Night achievement is: "Claim 10+ power on a single turn." If I follow the discussion on the new Stark agenda you can achieve these 10 power with power for unopposed and with plots and events. You cannot count the power that gets moved to your house card for the claim of a power challenge. You also cannot count the power for renown because not you claim but your characters do. Am I wrong? Am I right?

I think you're wrong. I think the idea of the achievement is just to get 10 power in one turn by any means possible, otherwise you would have to build a deck solely focused around getting that achievement.