How to Export full back up of entire database
Exports and backups serve different purposes: 'export' refers to an extract of data to use in another system, 'backup' refers to recovery in the event of system failure, recovery from bad user actions (eg unintended deletes), creating a second copy of the site etc.

If you want a backup, then take a dump of the mysql database with mysqldump or an equivalent provided by your hosting environment.  That will include 'all the details' including all activities, events, contributions, memberships etc relating to each contact.

If you want to export data into eg a spreadsheet, then there are a few options:


I think you were referring to the Export Contacts action from contact search results.  If you don't want its selection of primary fields then unfortunately you need to specify each one.
You could look at using a report (eg Constituent Report (Summary)) that allows you to export as CSV (in the Actions dropdown).
If the reports don't provide what you need and you are on Drupal, then you could create a View and use eg Views Data Export to create your own CSV.
If you have command line access you could also look at, and maybe customize, the script at &lt;civiroot&gt;/bin/csv/export.php