I've used TextureAtlas to group every part of the model together, I've set up a new UV in the editor, unwrapped the model, unticked Selected to Active, set up a new Image Texture node in the Node Editor, but I keep getting an error when trying to bake. It says that there's no active image found in material 'Iris' (for the eye). Not sure about this as everything has been selected, unwrapped and added to a UV image.
For each material added to the mesh from which you're baking, you need to have Image Texture node (selected, but not connected with anything ) with new image on which you want to bake the texture (f.ex. NewColorTexture.png, created in UV/Image editor or in Image Texture node Properties in Node editor). You can bake toon shading as easy as any other.