Use the attack behind an intervening piece.
A bishop, rook or queen may become an attacker when an intervening piece moves or is exchanged. Calculate that exchange before choosing the first capture. The important target is often behind the piece you can take now.
Trade rooks to open the mating line
Your rook takes the enemy rook with check. After the rook recaptures in this line, your rook takes it and gives checkmate.
2 more clean runs (at any point) to reach Recall.