* sftp your database dump to the server then
* drush @[site].[env] ah-db-import [/path/to/db/dump/file]
ie: drush @babsoncomm.babsond7dev --uri="dev.bell7.babson.edu" ah-db-import latest.sql --drop
in this example I specify the uri because the alias at Acquia wasn't specific enough out of the box, and then the --drop means drop all existing tables, so you can effectively just overwrite the database with the new sql in the dump file.