This is done by beating the penultimate (second to last) level of each painting, ignoring the last (400 teensie) painting.
You don't have to play any of the final levels (each one is a separate trophy). This is essentially "You have beaten the main game". After this, you will still have the retro paintings, the invades, and the final main painting (of the super hard levels), as well as the musical final levels.