Another way is to play through the levels and win as many scratch tickets as possible. Unlock the origin levels with these, since Origin worlds contain no invasion paintings. This way demands some patience and gives the player the chance to win a diamond cup without playing invasion levels, whose difficulty levels increase quite fast. Some are almost impossible to get all 3 teensies on.
Go forth until you unlock all the paintings from Jibberish Jungle. These aren't the most difficult levels and a little practice helps finding and collecting all the teensies. Still focus on collecting enough lums to unlock more scratch cards.