Well you've got the right type of ships. LRMs will mince the disciples and flaks will keep the strikecraft down. You might want a couple of Cobalts to destroy the carriers more quickly though. However just 20 frigates with your capitalship totaling 130 fleet supply is a bit small. Also you should probably get the third military lab to the the Hoshiko robotics cruiser to give you an edge.

Edit: no matter what though you should scout his fleet. Never hesitate to do so if you haven't seen it anytime recently. Also worth noting is if your scout reveals that most of his strikecraft are bombers, your flak will be less effective. Fighters are the only real fast way to get rid of bombers unfortunately, so carriers would be better than flak in that situation.