I would not recommend trying to solve this splendid problem, which was composed by JC van Gool in 1979. Just play through the solution and see how long it takes you to realise what is going on before you boggle at the final position.
Since Black has threats of his own (with 1...Bc6+ 2.Ka6 Bb7+ 3.Kb5 Qc6 mate top of the list), White has no time for quiet moves. It has to be checks all the way. Neither 1.Bxf6+ Kxf6 2.Nh7+ Qxh7 nor 1.Nce6+ Kh6! leads anywhere useful, so the solution has to begin 1.Nfe6+! dxe6 (fxe6 allows a quick mate with 2.Qg6+) 2.Nxe6+ fxe6. Now 3.Qg6+ Kf8 4.Qxf6+ Ke8 5.Bg6+ Kd7 lets the black king wander out of range, so the solution continues instead with 3.Bxf6+ Kxf6 when, instead of the natural 4.Qf8+? Ke5 5.Qg7+ Kd5 6.Qxg5+ Re5 7.e4+ fxe3!, White plays the subtle 4.Rxf4+! gxf4 5.Qf8+ Ke5 (5...Kg5 is mated by 6.Qxf4+ Kh5 7.Qg4+ Kh6 8.Qg6) 6.Qxf4+ Kd5 7.Qg5+ Re5 (7...e5 allows immediate mate by 8.Qg8) and now it's just a question of getting things in the right order: 8.e4+! Bxe4 (Nxe4 allows mate one move earlier). Now if Black's knight on d2 and rook on b2 were elsewhere, we could mate with Rd4+! followed by c4, and that gives us the rest of the answer: 9.Qxd2+! Rxd2 10.Ba2+! Rxa2 11.Rd4+! cxd4 12.c4 mate! A real tour de (minimum) force.