When students ask me for advice on drafting a cover letter, my best guidance is to start with an outline that reflects the theme or purpose of each paragraph. So many students simply throw together any information they think is helpful without attempting to organize it. Anyone who has ever been involved in hiring for a law firm (and I have) knows that a cover letter is a writing sample. So you must approach it the same way.
First, brainstorm about what makes you a good candidate for the position. Make a list, group similar items together, and find the common theme between them. Then begin that paragraph with a statement that summarizes what the purpose of the paragraph is. Next, list the specific details that back up your claim. For example, if you claim to be a good writer, be prepared to do more than just make a vague, self-serving statement in that regard. Discuss high marks you received on key writing assignments, how you were selected to assist a professor in writing a legal article, or how you obtained a writing certificate.
By following this simple outline with thematic paragraphs, you will prepare a well thought out, organized cover letter that will demonstrate your writing abilities and distinguish you from the other applicants.