I have 2 Ion Beams and a Heavy Ion, as well as a Pike Beam. What I did was focus all my ion beams on the triple rockets, which would have me either taking down the shields or disabling the rockets. I found autofire was bullstuffing me for the pike beam, always firing when the shields were up, so I manually used it whenever their shields were down.
They should add some augmentation where if an autofiring weapon can't do stuff at the moment, it delays the autofire until it can... Although then it'd be too easy mode, huh?
Edit: I also have a Anti-Bio beam in storage, but without my ion beams I can't take down the shields to use it. I know it'd be amazing against those starfishs in the weapons, but I'm not well armed enough to go without the ion beams.