Step 1

Let’s start outlining the artwork. There are many ways to do this.

Select your Pen Tool (P). Open the Stroke panel. Select a black Stroke of 0.75 pt, Fill to None, Rounded Caps/Corners, and begin tracing over the main parts of the artwork. 

As a start, trace the basic line work and leave out the organic shapes, curved lines, and ellipses.

Next, select the Ellipse Tool (L) with Fill to None and black Stroke, and trace over the ellipses in the illustration. At some points, you may need to select the Scissor Tool (C) to split paths at anchor points or along segments, and then delete the excess paths.