I think I found it. First I kinda found a mate in 2 but I don't think it's valid, since black isn't forced in any way, just I guess a natural thing to take the pawn?

a7 Qxa7
Rxf4#

Though if black actually wants to stop mate, Q can just go to e5 to keep protecting the f4 bishop, BUT

1. a7 Qe5
2. Bxe7 to threaten to promote, Qe7 to block
3. Bxf6+ Qe5
4. Rxf4#

Still not sure if this is it or if I missed something. What a great and terrible puzzle.