The archive contains an additional function: It is not possible to delete something in the lists of newsletters, subscribers, campaigns, mailing lists and templates. Deleting only is possible in the archive. Here, too: Mark the desired to delete in the appropriate tab at the select box and click on Delete at right top. Here also you have to answer a confirmation prompt. And also an additional question appears at campaigns to delete the assigned newsletters or not, too.
For deletion the permissions View archive and Delete are necessary.