The easiest way I know to do this is to create a separate artboard for each illustration. To do this, make sure each one is grouped together.
Go to File->Document Setup->Edit Artboards or just hit Shift+o to start editing the artboards. Then just click twice (not double-click) on each group to make a new artboard for each one, it will automatically size each artboard to the art. You'll probably want to delete your original artboard. If it's important that you save your original artboard, you may want to save the file as a copy of your original.
Then simply select File->Export, select PNG as your file time, check the box next to Use Artboards and make sure All is selected under that. When you hit Export it will bring up a dialog box that will let you select resolution, anti-aliasing and backgroundcolor options. When you hit OK it will output each artboard as separate files into your chosen directory, with the artboard number as a suffix for each one.
I'm sure there is a way to write a script to make the artboards for you, but unless you have many files like this it will only take a minute to set up the artboards, so it's probably not necessary unless you foresee doing this operation a lot.