The dance of the knight:
1.Ne6 threatens Ng7 # or if 1. ... Be5 2.Ng7+ Bxg7+ 3.g4#
1. ... Bf2+ only way to avoid the mate
2. Nc5 threatens g4# or if 2. ... Bxc5 3.Kb7 and 4.g4#
2. ... Bg3 only way to block the g-pawn
3.Nd7 threatens Nf6# or if 3. ... Be5 then 4.Nxe5 and 5.g4#
3. ... Bf2+ only other move
4.Nb6 threatens g4# or 4. ... Bxb6+ 5.Kxb6 and 6.g4#
4. ... Bg3 only other move
5.c4! threatens Nd5 and Nf6#
5. ... Bxc4 only way to avoid Nd5 path
6.Nd7 this move on the 5th move would have failed because of a later Rxc3 and at least another check on the white king (found this only after I tried that as the solution), now the bishop blocks this path
6. ... Bf2+ only option
7.Nc5 threatens g4#
7. ... Bg3 only option
8.Ne6 threatens again Ng7# or Be5 Ng7+ Bxg7 g4#
8. ... Bf2+ only option
9.Nd4 Bg3 (as above)
10.Kb8! here the absence of the Rxc3 and Rxc8+ becomes apparent. Now black has no defense against 11.Ne6, 12.Nf4+ and 13.g4#
edit: oops beaten while I was typing