The fault

I think I found the mistake: there(ru.lichess.org/training/37263) are solution to checkmate, but you should kill the queen - that's strange.

I do not see anything better than winning the queen. What is the mate?

Neither do I. But whenever I think I found a better solution then the one that is "correct", I check it in analysys with computer moves. You know, you just make moves for one side, and the ones adviced by computer are your opponent's responses - try it out, works for me every time.

PS: After you solve the puzzles (or make a mistake) you can find a direct access to analysys board from buttons below chessboard.
By the way, It always turns out I'm the one being wrong. ;)