Believe me. I've done everything in my power. I just have the WORST luck when I get to that battle. Like, a fire that spreads faster than usual, or a well placed ion shot at my shields. It's horrible. I cry.
Hmm...I'll leave what I've found out in FTL here.
-Cloaking helps, automatically dodges everything that comes your way and buys you time to get stuff working, as the enemy doesn't shoot at you.
-A crew teleporter + two Mantises/Rockmen would allow you to take out the weapon systems immediately, as there's only one guy each operating the weapons, and they are isolated.
-Ion=Missile > Laser > Beam. Ions disable shields, missiles ignore shields. Either way, both are dangerous.
-Upgrading engines first to at least level 5-6 is good, since they increase evasion chance. Also have a crewmember training in both the pilot's seat and the engine room. You should get about 45-51% evasion by the end. Also, it's a good idea to upgrade the pilot module, increases evasion chance, and gives you about a 1/4 to a 1/2 of your total evasion if you need to use your pilot for some reason.
-For fires, use a Rockman for fire suppression. Otherwise, open your damn airlocks and the doors of the rooms that are near the fire. Much more easier to cut off the oxygen than to fight the fires. Also, consider turning off your oxygen supply if you really need to put down the fires fast. Upgrade your doors, too; they slow down the rate at which the fires spread (and the rate on how fast invaders get to your systems and start attacking your crew.)
As for the mothership, conserve your ammunition.
It's a three-part battle.
