1. Q-c7+ Kxc6 2.B-b5+ picks up your Queen. You're lucky he blundered. In fact, after Q-c7+, no matter where you move, you drop the Queen on a1, as the Bishop comes out with check.
Move Choice

First I assume you meant 1. Qc7+ Kxf6 2. Bb5# and while that's true I could've diffused the situation by playing Kg8,Kf8, or Ke8, and if I did play Kf8 I could've diffused the threat of Bh6+ by playing h6.
In this position should what should my opponent have done to try for checkmate or a draw with me playing as black?