The import process went smoothly because there was hours of work prepping the Illustrator file. The problem you will have with most conversions are compound paths. These are objects with holes, all compound paths must be divided into shapes without holes. 

This proved challenging when coming from a large Illustrator piece. My strategy was to divide the art with a 10x10 grid, and clean divide any remaining compound paths into individual shapes. Any text or simple areas I did by hand, but the grid division really helped break down the rest of the image.

Here is an example of some of the grid cuts in Illustrator.

After the layers list included no groups and no compound paths. I went back over the art and combined any shapes that didn't need to be divided. This step is probably not needed but it made the file look a little neater and I was concerned with all the cut lines converting correctly.