Do you mean this one? It's a domination scene from the same mines you explored for the Miko dress in Ayane's quest.
As for the sword, during the blade's reforging, you can pick one of the paths between brute force, magic power, and balance. The final sword will have the stats you pick. So, while you pick one, other paths become unavailable. The lab upgrades just list all possible options.
And, no, Ikko island has its share of domination scenes for normal enemies.