You can read up on some drush specific tasks that you can do in this Elevated Third blog post
Acquia supplies drush commands and aliases that tie into Acquia Cloud API calls. So you can actually simply use the alias and the
rsync drush command:
drush rsync --progress @sitename.env:%files @localenv:%files
You can also create and download Acquia database backups with the
Also, if you want an "all-in-one" solution, the newer versions of Acquia DevDesktop tie directly to your Acquia cloud account and can get database and file syncs automatically.