Speaking of accomplishments.
Your resume as noted above is a great place to show relevant experience and skills. Since you have to keep this letter short you’ll need to pull out the best ones.
Find the skills and accomplishments that are the most relevant and impressive and provide some additional details about those in your cover letter. Try to relate them directly to the position that you want.
If you can get testimonials or positive feedback from previous bosses or coworkers try and work that in. It’ll go a very long way.
Most positions you want are going to have you apply electronically. This can either be via an email or a website.
If an application asks for a cover letter, you are best off adding an attachment to your email. This will show you know how to follow instructions. In those cases, you might want to create a small note in the body such as: “Dear Jane Doe, Please find my application materials for XYZ attached. Thank you for your consideration!”. Be sure you attach your materials in PDF form. Use a PDF so that you know they can open it and avoid sending a Word document unless asked for one.
In the event they say they want no attachments you will paste your cover letter directly into the body of the email.