Argh... I had Kc7 before Bxf3 -- it almost works too. If black plays either Qxb5 or Qa7+ he loses... but Qf4+ refutes it.
One way to mate, 2 ways to get mated

Yes got it.. only one way as Q is pinned and can't allow any free move to Black.. Nice one.. I played BxR last move instead of QxR.. ok i suppose..
What about 2... Re1, after the king reveals check, cant the rook block and queen recapture?
After 2. ...Re1 3. Kc7+ Re4 4. Bxe4 Qxe4, 5. Qb8 is checkmate.
What about 1...QxQ+?
That move is most definitely illegal.
If you meant 1. QxQ+ (a.k.a 1. Qxa4+), then White can't stop Black from escaping to a6 after taking back with the rook.

No, I mean to save black, black to move. The black queen takes the white queen on b4. I can't see a checkmate with the two bishops afterword, and if white survives that, then he's got two rooks on two bishops.
Oh, nevermind. I do see a checkmate. 2. Kc7# *sigh*
No, I mean to save black, black to move. The black queen takes the white queen on b4. I can't see a checkmate with the two bishops afterword, and if white survives that, then he's got two rooks on two bishops.
Oh, nevermind. I do see a checkmate. 2. Kc7# *sigh*
Okay, I see what you meant. There's still problems there though.
1) The move is 1. ...Qxb5+, not 1. ...Qxb4+
2) 2. Kc7 is not even a check, let alone a checkmate. Even if the knight wasn't there, Black would play 2. ...Qb7, and still be winning.
This is a puzzle with only one way to win. White is able to win inspite of material deficit. Solve to see. I have also provided some variations for you.