During the game you will earn coins by smashing objects. At the end of each act you are given the option to upgrade your characters (though you can do this at any time by pressing the back button). Once you’ve got all the powers upgraded for any of the characters, you’ll get their achievement. You can only upgrade a certain amount depending on where you are in the story. This will probably take 2-3 playthroughs, and must be done on the same difficulty, so do not start a new game until you are done with this, just keep replaying levels.
I would suggest doing Military Base, Act 1. This seems to net the most money each time.