You could use Diceware
to create a strong passphrase. Since the diceware method creates a passphrase composed of several words chosen randomly, they aren't hard to remember.
Some may disagree with me, but I think there is really nothing wrong with writing down a password, so long as you treat it like you would your credit cards or cash. Keep your password written down in a safe place, like in your wallet.
You said your concern was mainly attacks over the network. Since you said you are using RSA key pairs, I presume the daily hacking attempts you referred to are via ssh. If you disallow password login in sshd_config by specifying the "PasswordAuthentication no" option, and you have enabled RSAAuthentication and PubkeyAuthentication, then you don't need to make your local console login password so difficult that you can't remember it because no one will be able to login via ssh with a password. Even if someone knew your password, they couldn't login with it via ssh if PasswordAuthentication is disabled. You might consider also setting "PermitRootLogin no" and limit which accounts can login with the AllowUsers option.