In order to get the Mew avatar you must feed 75 Kadoaties at the Kadoatery. It takes a lot of pratice and quick handwork to feed ’em, but hopefully my page will help you get a little better at it. The screen shots below are how I managed to feed them, and is one of the easiest ways to do it I believe.
The Kadoaties restock around every 30-35 minutes, sometimes with a ‘mini restock’ in between (which consists of one, sometimes two Kadoaties, that become hungry in the lower right hand corner). This happens when a Kadoatie with an unbuyable hasn’t been fed from the last round (this Kadoatie will usually be in the upper left hand corner). So with the added mini restock, it essentially makes the new round a full restock. These usually appear anywhere from ten minutes after the initial restock, or around five to ten minutes before the next restock.