To do this, you're going to have to just kill yourself multiple times. The trick of this level is to try to avoid all the studs you can, I got through the level with just over seven thousand studs. I probably could have hit six Thousand if I really tried.
Once you get to the end, you'll swing down and get to a boat with a steering wheel. At this point. that's the end of the level. Do NOT trigger the steering wheel yet.
Jump off the boat or switch characters to one still near the main land. The reason for this is jumping off the boat will get you eaten by a shark, which does not loose studs for some reason. However drowning yourself (by submerging yourself and not letting up) will drop studs. Do that until you run out of studs. Note, sometimes you'll pick up studs as you die. That's ok, just kill yourself over and over.
Once your stud count is 0. Go back to the steering wheel. If you pick up a stud while walking there, you'll have to go back and drown to clear those studs.
It's a very annoying process, but after you do it all, the trophy will pop as it tries to add your 0 studs to the total...