A cover letter is not a resume. Focus on a few relevant things you think the employer must know about you. Remember that stories are Context—Action—Results (CAR). If the results weren't great, focus on your approach and process and what you gained from the experience. The overall tone of your cover letter should be this is what I can do for you.
A cover letter which recites one's experience in reverse chronological order is a duplication of the resume. Second: “You shouldn't use anything from your resume in a cover letter.” Wrong again - you don’t need to come up with totally new material. A cover letter which is completely unconnected to the resume may do you a disservice if the letter and resume are ever separated.