GPA: 4.1 Weighted, 3.7 Unweighted
ACT: 34 (super scored)
National Merit, some varsity tennis, a summer engineering internship of sorts, various science related clubs, no significant leadership positions to speak of.
I can tell you right now that I was probably one of the least impressive students there resume wise, so I might make a good benchmark. I think I wrote very good essays, which is what got me to the competition. There were multiple students with perfect SATs, a student who grew up in a missionary in Africa, and a student who participated in research in Taiwan. So as long as you have solid stats (i.e, at least as good as mine), then it seems you just need a few other points to stand out as well
However, once you make it as a distinguished scholar (the top 100 or so applicants), it doesn't really matter anymore. Everybody receives at least a $21,000/yr scholarship, some win full tuition, and somewhere between 10 and 30 students will win a DuPont. Once you're there, the only criteria is to be personable, portray yourself as intelligent, and try to show as much interest in the university as possible. Hope that helps.