For Illustrator features we don't currently support natively as vector, you can use the "Render As Image" option for the artwork skin. Expand the Parts folder until you see the skin (it'll have a picture icon and named the same as your .ai file). Select it, then enable "Render As Image" in the Properties panel. Note that this option disables Wiggler (if applied), but should allow things like line weight, gradients, etc. to work.
Let us know if that works for you. Thanks.
You can also do this without involving the Parts folder (which will be hidden in Preview 2) by selecting any skin layer in the puppet panel: double-click the puppet to open it in the Puppet panel, and then twirl open subpuppet groups until you see any skin layer (gray square icon). Select it and that same "Render As Image" option will show up in the Properties panel.
At the current time, there are some features of AI that we don't support. If you're not getting identical results in CH, open your puppet in the Puppet Panel, select a layer, and click "Render as Image". This will rasterize the artwork before we start to manipulate it.
The Wiggler behavior will no longer work and since it's no longer a vector, the edges won't stay super sharp if you zoom WAY in.
We may consider turning this on by default.