Solution
1… Rxg2+ 2. Kxg2 Rf2+! (overloads the c2-Rook) 3. Rxf2 Qxc1
Or
1… Rxg2+ 2. Kxg2 Rf2+! 3. Kh1 Qf3+ 4. Kg1 Qg2#
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1… Rxg2+ 2. Kxg2 Rf2+! (overloads the c2-Rook) 3. Rxf2 Qxc1
Or
1… Rxg2+ 2. Kxg2 Rf2+! 3. Kh1 Qf3+ 4. Kg1 Qg2#