I wondered how to achive killer king achievement
yk two rooks or queen mate? get your king in the backrank with the opponents king, then slide your king behind the rook above, checkmate via king!
It's all about "discovered check". A king giving the discovered check-mate is a killer king. Castling also counts as a king's move and get's you the award if it checkmates.
Technically no chess unit ever hands a checkmate since checkmating is attributed to (a) the player (b) the move - but not the piece! But chess players have adopted the habit of acknowledging the owner of a checkmating move as the checkmating piece! Which is OK as long as you understand that that applies to the king as much as to the other pieces! Thus: killer king.
Note that it is does not matter which piece(s) check in the checkmate. It's only about the owner of the checkmating move!