Following the hardening theme....
What are some best practices, recommendations, required reading for securing MySQL.
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I suppose the usual OS methods (including fail2ban if remote ssh admin is required), then block all external access to the MySQL port, or allow a whitelist to connect if absolutely necessary. Set a password for the mysqladmin user.
After that, the mysqladmin user should only be allowed to connect from localhost and should be the only user granted any privileges via the 'user' table - all other users denied access by default (i.e. in the user table) but given specific grants to individual databases.
Note that you should not expose MySQL directly on the internet. If you must have remote data access use a VPN (e.g. stunnel with client verification).