Every seventh enemy kill spawns a bonus item instead of a fruit, but this can be manipulated to a degree. To guarantee spawning the turbo item on Round 2-4 do the following:

Round 1-1: Only kill the Boomer Roomer on the top platform to the right of the warp and then take the warp to Round 1-4.

Round 1-4: There are four levels of long platforms after you emerge from the water and jump up three one-block platforms. Jump from the first long platform to the second platform, shoot the two (2) Flamer enemies.

Jump to the third platform. Three Flamer enemies will appear on the fourth platform. Allow them to go past and then jump up to the fourth platform and enter the warp zone to Round 2-4.

Round 2-4: Progress until you get to the door that spawns two Boomer Roomers and a crab. Shoot the first Boomer Roomer to spawn the turbo item.