2nd/7th rank are always critical in endgames. But even when there are a lot of pieces on the board, these ranks are still important, like in this position.
Black Rook and Bishop are invading on the 2nd rank, and fix the King on c1. Although our Rook is under attack, there should be some tactical opportunities here.
Rxc2+ is not good, because white Bishop on g6 will take. It will in fact introduce one more defender back to home. Nb3+ is a nice candidate, but it's premature. Our Bishop on h8 is a powerful piece on a1-h8, but that diagonal is too crowded.
Because our King is also exposed to white Queen and Bishop, and white is attacking our Rook and Knight, we may have to do non-stopping checks.
Qe3+ looks nature. If Rd2 block, we will have a back rank mate. So Bd2 block is a must. Now one less piece on the a1-h8 diagonal but one more piece on the 2nd rank.
Two possible checks here, Nb3+ and Qxd2+. Nb3+ leads to nowhere because the distracted c2 pawn can be easily replaced by Bishop on g6. So Qxd2+ must follow. Rxd2. We have two Rooks that can go the back rank, of course we want to activate our back Rook, Rf1+, Rd1.
After these moves, the progress we have made is that we removed the Bishop on c3. If you can see that pawn on b2 is the key, you will see the problem. Our Knight is blocking the diagonal and c2 pawn is blocking the 2nd rank. Can we remove both?
Back to our candidate move Nb3+, you should see the mate on the next move.