This is the hardest achievement in the game. For this, you don't need to get all of the smiley murphy faces (though it is recommended), but you need 100% or five stars at the end of every chapter. To make sure you meet the unknown score requirements, explore every level before grabbing any gems or defeating any enemies and come up with a strategy to make the biggest combo you can get using power-ups (you get 2x points while using one!). While you are making a combo, grab the yellow gems first and keep the best stuff (like green gems) for last - but if you're using a power-up, make sure this doesn't run out before you've grabbed everything! This will allow you to score extra.
See end of guide HERE for a chapter by chapter breakdown of how to get the highest score possible.