I enjoyed this grid but don't think that Adversary, Bete Noire, Rival and Opponent are equivalent to "Nemesis" They are, basically, just someone that is against /opposing you except Bete Noire which is something that you dislike... I found all the groups and connections.

For me, the desserts were easy, and I thought the list of enemies was easy though I had not accounted for bete noire. I decided not to click on the enemies in favor of trying to find one other grouping. I noticed three very strange words and then tried them with others, finally getting Pains as the fourth. Then I tried the enemies list and got the wrong four. Finally, I saw the Star Trek connection and was able to complete the groupings. And then I noticed the letter rotation for the countries. Nice construction!

Really enjoyed this one. Because Bete Noire is a little different from the other three, I think there should be some leeway in the answer options when looking for a word that covers all four words.

"move the letters" are never enjoyable, consider this a sign from God