Since the maximum power output of a ship's reactor is 25, unlocking this achievement without Advanced Edition requires a fully upgraded reactor plus 4 Zoltan crewmembers manning systems to provide 29 power. Note that it is possible to achieve without a fully upgraded reactor, but more than 4 Zoltan crewmembers will be required.
A lot of scrap is required for the achievement, specifically, to sufficiently upgrade the reactor as well as the systems to use the power. Subsystems do not use power, so upgrading them doesn't provide any benefit.
The Backup Battery, introduced in Advanced Edition, can temporarily provide 2 (or 4, if upgraded) power and make getting the achievement easier.