Doge Jump

The Bandit's Way flower is optional, as there is another flower available later that does not affect your route, but your Croco fight can be much faster if you do get it since it enables you to skip some of Mallow's turns.

To get it, you will have to grab the star, jump off the top of the K-9 (2-3 frame window), and hit the box when it is at the bottom of the oscillation.

Watch how the K-9 in the upper right blinks. When his eyes go black for the 13th time, advance the final text box, and then the Flower chest should be on a good oscillation cycle. (This is easier in Japanese because of the faster text.)

(video credit: Lack)

In this GIF, two frames you can jump on are indicated by the large "B". You can do this on the final frame of Mario's falling animation, or the first (and only) frame of his standing animation.

The window is slightly more forgiving depending on where on the dog's head you land.

(image credit: pidge)