To start with this, you need to complete Entropy missions until you're given Aggression Must Be Punished. The next bit under a spoiler tag will make things easier, but just in case you don't want to see it...
While doing this mission, naix will contact you and attack. Once you've recovered, check the logs on your PC to track him down. Once you get to his root gateway, delete his files to receive an email from him. This starts the third set of faction missions.
Eventually, you'll reach the /el message board. The top messages will be about trials. Connect to that IP address, hack it, and view /web/index.html to get the IPs of four trials. Keep around four shells handy, you'll need it for most. Your goal is a file in each home directory starting with Reward. It will have a number inside. scp the files or write down each number.
Trial of PatienceSet your shells to overload, then wait. I got up to grab a snack. It'll take a while.
Trial of HasteThe trick here is learning how dc can help you evade a fast trace. Each time you commit an action, you can disconnect and slowly open the ports. Break the proxy, disconnect. Hack one or two, disconnect. Hack the last, disconnect. PortHack, disconnect. Once it's done, you're in.
Trial of DiligenceOnce you're in, scan the network to find the Tail of Diligence. Hack into that to find the Reward file.
Trial of FocusNothing out of the ordinary here. The firewall takes a long time to analyze, so once you're done with it, disconnect and reconnect to reset the trace.
With all four rewards, you can put together the IP address. While this is a static IP, you can only use it to get a particular piece of software early; you can't skip half the game with it. Pick up SQLBufferOverflow from home/Gifts, and your session should save, followed by a few emails and the achievement.