You can target a specific category page using the body classes in WordPress.com blog.
For example, you could use this to add a description to the Accomplishments category page:
.category-accomplishments #container #content #main .archive_header:after {
content:" - This is a description for the Accomplishments category archive page.";
}
You can add a picture as a background image. How to configure the CSS will depend on the size of the image. Here's a starting point:
.category-accomplishments #container #content #main .archive_header {
background: url(YOUR_IMAGE_URL);
}