The secret is to overcap weapons power + beam arrays. That is, do whatever it takes to push weapon power well above 125 and beam arrays will suddenly deal a lot more damage. There are lots of ways to do this, Weapons Battery, Emergency Power to Weapons, Auxiliary to Battery, Energy Siphon, EPS Power Transfer, [X->W] Warp Cores, Borg Assimilated Module, Zero Point Energy Conduit, Red Matter Capacitor, Plasmonic Leech Console, etc..
Nobody really knows exactly why this works. Some say each point of power above 125 adds more damage to beams, others say the additional power provides a buffer against weapons drain and makes beams do their maximum damage. All we know is the effect is a significant boost to beam array damage. Stack on Attack Pattern Alpha, Beta or Omega for even more damage, Fire At Will to attack all ships in range and watch your dps climb to crazy heights.