I can't possibly tell if it's always a mate in 10 with best play for black, just too many lines. But even starting with 1.Nd8+ makes the situation look very bad for black, I think.
For example, here's an easy way black can lose in that line 
1.Nd8+ Ke7 2.Qc8 Qe2 3.Qxc7+ Ke8 4.Bxe2, and this ought to lead to a mate pretty soon, I think. (edit: Oops! Scratch that, I missed the black knight on d7 in your diagram ... sorry. Try instead: 1...Ke7 2.Nc6+ Kf7 3.Bc4+ d5 4.Nd8+ and it's looking bad, but not yet a loss.)
So starting with 1.Bc4+ and following with 2.Nd8+ after 1...d5 ought to be even stronger.
1...Qd5, of course, fails immediately to 2.Bxd5#, as I'm sure you saw already. So in your line it would be a matter of finding a forcing line for everything black can do after 2.Nd8+. White has an awful lot going for him, I think, so it should be possible.
For example, here's a line that looks promising, though I don't think this is the best play for black.
1.Bc4+ d5 2.Nd8+ Ke8 3.Re1+ Qxe1 4.Nb7+ Nb8 5.Qxb8+, and if 5...Kd7 then there follows 6.Bb5+ Ke7 7.Qxc7#
I'm so perplexed on this puzzle, I've only seemed to solve that the first move is Bf1-c4 and it's suppose to be white to mate in 10 moves. This puzzle is driving me crazy, and I'm dieing to know the possible solutions. I'd greatly appreciate any help anyone could give.