Rematch with Koopa the Quick is the third mission of Tiny-Huge Island.
Proper lag reduction at the start of the level will save about 3-4 lag frames, or two real-time frames. The inputs are C-Right, then Mariocam C-Down & C-Left.
Note: this video shows the proper lag reduction for the ending. Make sure to stay in Mariocam C-Down, and keep the camera facing the out-of-bounds area.
This video explains the RNG that affects how fast Koopa the Quick finishes the race.
Doing a ledgegrab on the very edge of the platform here can manipulate Koopa into stopping earlier. You can also just stand near the corner without ledgegrabbing. Get up right as Koopa crosses the bridge.
This route guarantees that no balls will get in Koopa's way during the race, so it might give you faster times on average. This is explained in more detail in the above video.
