From the Super Mario Wiki, the Mario encyclopedia
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The player first has to use a wire to swing up to the Mini-Mario, and then fall back down with it. After passing below a Brickman and its debris, the player has to continue right and use a Springboard to get onto the upper platform. While avoiding the Katakata Spanner Heihō's projectiles, the player has to move left and use another Springboard, allowing them to reach the locked door.