I don't think a pawn breakthrough works because the white king is in time to stop any pawn that gets through. 1...a5 2.bxa5 b4 3.axb4 d4+ ( surely not 3...cxb4 4.cxb4) 4.cxd4 cxb4 and now whites king is in time to scoop up the b pawn and since he now has the farthest outside passed pawn he wins. If on the other hand 1... a5 2.bxa5 Kc6 was the plan then I guess it's actually more straight forward than the continuation I would have played.
( 2.Kd3 dxc3 3.bxc5+ Kxc5 4.Kxc3 a5 5.f3 b4+ 6.axb4+ axb4+ 7.Kb3 Kd4 8.g4 fxg4 9.fxg4 hxg4 10.f5 Ke5 )
( 3.f3 Kd5 4.g4 hxg4 5.fxg4 fxg4 6.f5 g3 7.h5 g2 8.Kf2 c3 9.f6 gxf6 10.h6 c2 11.h7 c1=Q 12.h8=Q g1=Q+ 13.Kf3 Qce3# )
3...Kd5 4.Kc3 a6 5.f3 g6 6.g4 fxg4 7.fxg4 hxg4 8.f5 gxf5 9.h5 g3 10.h6 g2 11.h7 g1=Q 12.h8=Q Qc1#
I tried to put this into a pgn but it doesn't seem to be able to read the variations. I'll leave it like this if someone knows how to get it to work.