Without a shadow of a doubt, the best way to get studs are as follows:
Firstly, play through until you save up enough for invincibility which is found on Chapter 5 of Episode 4. Using invincibility you'll no longer lose studs.
But that's not where it ends. Next save up for the "X* score" extras. Obviously, start with X2 score and make your way up. By switching on all the X score extras that you have on, your stud collection will sky rocket. By purchasing all five X score extras and turning them all on, one silver stud is worth over 3500 studs!
Hope that helped.
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