This achievement is easiest with a laser weapon and two beam weapons. Firstly, use the lasers to disable shields, or at least destroy them for a few seconds - ONLY use the laser weapon when the beam weapons are fully charged. Then, use your beam weapons together to hit every room of the ship before the shields regenerate.
The easiest enemies to get this achievement from are those with short ships, for example, if you find an automated defense ship, since they only have 5 rooms, you can hit them all fairly easily. In terms of the best weapons to use, the pike beam is capable of hitting the most rooms at once, but you can use shorter beams for this achievement so long as you can find a short ship.