AFAIK, the way that he gained access to these accounts wasn't anything particularly impressive. I haven't been keeping up to date with it, and I've only skimmed over it, but it seemed like it was either a social engineering a representative of Twitter which allowed them to gain access to the internal tools, or they simply compromised one of the staff of Twitter. This might have been a simple way of gaining access, and there's no reason to believe that this was a particularly impressive feat.
According to the official
Twitter support, the attackers have targeted an employee via a "phone spear phishing" attack.
How such an attack could be performed is described
here, for example:
- A Twitter employee could have received a message on his phone to call a certain number
- The employee is then forwarded to a fake helpdesk employee
- The fake helpdesk employee uses social engineering techniques to trick the Twitter employee into handing over his access data