To get a Golden Ballsy trophy you must collect all 12 Silver Ballsy awards on each episode. Each level has 3 awards.
First you will need to pass each level in a specific time. You can see the required time in the award description. Not many of them are hard, but a few of the later ones will take a touch of practice. Play on easy to reduce your stress as obstacles move slower and the time penalty for failure is much lower.
Next, you must collect every ring on the level. See "All the rings in the world" for more details.
Finally, you will need to pass the level on Black and Blue difficulty. See "That was easy" for more details.
You do not need to do all of these is a single runthrough, all you need to do is meet the requirements and finish the level to get credit for the individual Silver Ballsy.