In order to
delete all contacts form iPhone, you have them syncing with another source (gmail, windows contacts, Yahoo, etc.) then in iTunes, select your iPhone under devices (left side), go to Info (top), deselect "Sync contacts with".
When you do this, it will ask you to remove your contacts or not. Click on "Remove Contacts", and then Apply (botton right).
If you don't have your contacts sync'd, then you can either setup a temporary sync to
iPhone Data Eraser that you have access to and then do the above, or do them one at a time.