I think I have the first couple of moves, but I can't quite see how to finish it off.
What I have determined is that white must continually check black, else black will launch a counterattack and white won't be able to do it in 4.
The queen on f seems like the best launching point, as there are two queens attacking it and it does give check.
1) Qaxf2 Qgxf2 2) Qfxf2 Qhxf2 3) ???
This is where I get stuck as to how to continue.