Killer King isn't that hard. You can set it up if you have a big material advantage and an opponent who won't resign.
Castle Victory is hard because you have to play for it from move 1, and often you will be forced to move your King and Rooks before you can execute it.
The problem is that I'm low elo (I'm 463 in rapid) so if anybody is at a disadvantage, they'll just resign making it nearly impossible to get.
Here's an example of somebody who resigned after I took their queen:
https://www.chess.com/analysis/game/live/107349572970?tab=review
In my opinion, I think either "Killer King" (delivering checkmate with the king) or "Castling Victory" (delivering checkmate with castling, might also give you "Killer King" achievement but haven't gotten it myself) because you need to set up the opponents king just right.