Should a undergraduate rely on PhD students to publish papers or do it individually? I am a undergraduate student who is trying to publish something so as to facilitate my PhD applications in the future.

I have a few seniors who help out in the lab and have been included as non-1st authors in some publications. Basically, what they do is helping the PhD's do some implementations. Thus, actually there is not much real research involved. But at least in the end, they are the authors, although not 1st authors, of some publications. It is quite nice for undergraduates to have such publications.

As for me, I am currently working on an individual project under a supervisor, who is extremely busy every day. Instead of being a helper, I am actually initiating the research all the way. I am also working towards publishing a paper to present the work.

Nice as it may sound, I am facing a lot of difficulties. As a undergraduate, my knowledge is so limited, and meanwhile I have to attend lectures. My time is also very limited. So I am really afraid I can publish nothing at the end of the research.

Since I have already started the research, no matter the decision to initiate one project my self is wise or not, I have to fight to the very end. 

Could anybody help give some suggestions to make my work get published more likely?
One alternate strategy that could help is to see about trying to present a poster of your work at a conference. Even if that doesn't have quite the same prestige as a paper in a journal or an accepted paper at a conference (if you're in CS), it still is a sign of doing significant amounts of research. An especially good sign would be if you could win a "best student poster" or "best student talk"-type award. 

However, the important thing for you will be to be able to discuss what you have done with authority in your statement of purpose to graduate schools, and to get a good letter of recommendation from your advisor that clearly outlines your contributions to your project. Having a publication is nice, but it's not an essential component for graduate school admissions.