I would like to access mysql via ssh terminal on a deluxe hosting package. Is this possible or do I need the 'ultimate' package or a vps or dedicated server?
This can be achieved with your cPanel hosting account. Check out this article: https://www.godaddy.com/help/importing-mysql-databases-via-ssh-7588
You don't need to use SSH!
If your database is set up to allow remote access then you can use
mysql -h yourdatabasehostname -u yourdatabasename -p yourdatabasename
from the command line on your own pc. You will be prompted for your password.
You can find the details (host, dbname etc) in your database management section on godaddy.
If you are using cpanel on economy hosting then you need to use your cpanel credentials
mysql -h yourdomain -u yourcpanelname -p yourdatabasename
you'll also need to add your IP to to the allowed list using remotesql in cpanel