Count yourself lucky, because this artwork is very basic and straight forward. This is basically a bunch of vector shapes stacked on top of each other; accented with gradients shapes. One just appears to be the mirror of the original. Time consuming but completely doable.
Depending on how clean the raster(bitmap) image is, you could perhaps do a image trace in illustrator, but there are tricks to preparing a raster for a clean trace. You can PM if you would like some help