Here's White's first move, Gxd6+.
Black has one legal move, Kf3. White then mates with Gh2:
Here's Black's first move, Gd2+:
White has two legal moves, Ka1 and Ka3. In either case, Black mates with Gc2. Here's the final position when White plays Ka3:
Here's White's first move, Gd5+.
Black has two legal moves, Kc8 and Kb8. If White plays Kc8, Black mates with Gxa8. If White plays Kb8, Black mates with Gc6. Here's the final position in the latter case:
Here's Black's first move, Bxg2+: White has one legal move, Kg1. Black then mates with Gh3: