How to import a live Drupal site into Acquia Drupal Dev Desktop?
First, use the Backup and Migrate module to create a copy of the database. Then download all the Drupal site files to your machine as well.

You can set up a local version by using the import option Acquia Drupal Dev Desktop instead of creating a new site and importing the Drupal files you just downloaded. 

Then use the Backup and Migrate module again on the local site to synchronise the database.