Creating Anime Embroidery Designs

Hi! For the past few weeks I have been attempting to teach myself how to create designs meant for embroidery on Adobe Illustrator. I have seen many different videos on how to turn anime characters into designs ready to be embroidered on an embroidery machine. However, I cannot figure out how to do this properly because every time I attempt to use the image trace tool, the design is always has colors where I dont want them, missing certain lines or the colors are wrong. I am very bad at explaining myself so I searched up an anime embroidery design example and the before picture to give you an idea of what I mean. The artist was able to transfer the image to embroidery with simple colors and all of the lines connect, but when I attempt something similar it doesnt work out for me. The artist was also able to add the purple outline and remove the black lines which I cannot figure out how to do. What's the best way to go about this?