Before you can focus on selling yourself you first need to try and see what the company is looking for in their employees and what is their area of expertise. You need to see what they want and the only way u can do this is by putting urself in their perspective. For example, if i was applying for a job, say at a criminal law firm, I'd firstly consider what sort of skills I have that they despearately need. For me, I'd sell the point that I'm very good team worker and back this up by at least 1 or 2 peices of evidence. I'd then go on to summarise why I believe having good teamwork skills will benifit the firm.
So to summarise, begin with something that the company desperately desires. So in your instance, the fact that its the biggest company in your area, means you can talk about your international business degree as allowing you to research in depth the impact of international factors on businesses. Give examples.....and then relate them to the particular company.
In terms of your skills Im sure you have various things like teamworking, communication, writing skills etc that the company might be interested in. It's your job to really highlight those factors that could really interest the company.
I can't really give you much more advice unless you are more specific about the nature of the company and the sort of things you've done that may stand you out.
Good luck and remember the key is to think about what, for that company, will make an applicant stand out and then to taylor your cover letter to this.