Tried the academy first, but it wasn't of much help.
Im mid way into the romulan mystery series, and have encountered a warship and i don't stand a single chance against it. It can destroy me in seconds if it shoots in a certain order. I can at most knock out 1 of the 4 simultaneous plasma torpedoes and it still does ALOT to my hull. I use my bridge officers to repair my hull and shield, but it's just not enough. The ship nukes me to kingdom come and i get it at max down to 30% before i die. I have the exploration cruiser with 2 photon torpedo launchers and 2 photon array or something in the front which i keep nukinig it with, but it's also the fact that it repairs its shield all the time so when my buffs run out it's game over.
Avoid being in front of the Warbird at all times. Attack it from behind. Stay away a little so you have time to destroy the plasma torps if necessary. I recommend Beam Fire At Will, a tactical skill that will take care of the plasma torps.
And some general advice. One torpedo in the front and one in the back is more than enough. The remaining weapons should be beam arrays for broadsiding your enemy.