This stage is Big Bounce Byway (4-4). This complete walkthrough will provide you with a 100% video playthrough and a screenshot of where you can find all the green stars. The best power up for the stage is Fire Flower to take out enemies at a distance.
Game Play Walkthrough Video
Green Star 1
You will see your first Green Star at the top of a mountain. Kill the three metal looking creatures for one of them to turn into a spring. Note that the spring can turn back into the creature after certain time. Jump on it to bounce higher and grab the star. Now, do not let go of the jumper yet, bring it with you to the second star.
Green Star 2
You can get this star with either of the two ways, the first way is to bring the spring thing across the platforms so that you can use it to jump to the platforms. The second way is to use Luigi to jump higher to the platform. After a couple bounces you will grab the second green star.
Green Star 3
Enter the purple mystery box when you see it. Kill the metal spring enemies for a spring to jump and grab the green star.
Near the end of the stage you will see the stamp being surrounded by circle flying bugs. If you still have your Flower Flower you can clear out a good handful of them. Simply grab the stamp.