To speed up combat, make sure you run on the attack power setting, 100 power to weapons and 50 to shields. The power level with the strongest impact on your combat ability is usually weapon power.
If you have trouble surviving in that battle, find an Engineering Bridge Officer. Train him Emergency Power to Shields I and Emergency Power to Shields II, if he doesn't already have it. Now use one of the two powers when ever they become available.*
If that still is a problem, don't forget to use distribute Shields (click on the middle of the shield UI, this automatically transfers shield energy from the stronger shields to the lower).
If it is still a problem, consider a Science Bridge Officer with Transfer Shield Strength and Hazard Emitters, and a Tactical Bridge officer with Tactical Team (Tactical Team is like Distribute Shield Power, but on steroids). And maybe Beam Fire At Will to deal with those Fighters more quickly. ▄
If it's still a problem, we might have to go back to the basics? Do you have some Mark X or better shields equipped (any type will do, but Covariants are probably best. The more [CAP] mods, the better.)
If it's still a problem, post your build and we will figure out what's wrong. (Probably )
*) TO get the most of the skills listed, you not only need to rank the power on your Bridge Officer, but also train the correct skills (you don't have to max it all, if you have trouble covering the ground and space skills you think you need)
Emergency Power to Shields: Warp Core Training, Shield Maintenance, Shield Efficiency