In that case, you should be prepared for lots of editing. This image with a contrasting background is relative easy to trace and edit. Sometimes, using color range in photoshop to "extract" a color or layer, then vectorizing each layer helps.
You can also try "sketching" the image in photoshop first.
Here is a simple and rough sketch of the image. You may need to try different settings and may need to do more than 1 sketch and combine them to get the details you want. After tracing them, you may need to edit the vectors to remove the noise and smoothen the curves. Most likely, you also need create new outlines to get better details and to define or contain the colors you want. A pro should be able to do that in less than a day as the image is not really complex.
But if you do not have the time, patience or skill, and if your printing volume justifies it, better just outsource the job.