Have you upgraded your shields, weapons, and consoles to the right Mk for your rank? Do the Breen Featured Episodes to get the Breen Ship Set every rank. You can also do the first Romulan FE The Vault to get Scorpion Fighter device that has 50 charges. It launches 3 scorpion class attack fighters.
Here are some tactics that should be used when fighting these ships. Plus also some abilities to consider. I am also posting links at the bottom of this post, to STO wiki. So you can look at abilites/powers ingame, and also the abilities of the D'deridex.
Do not fight a warbird head on, they use Tractor Beams to root you then hit you with a High Yield Plasma Torpedo. They also have Viral Matrix, which attacks subsystems apart from shields. Attack it from the side, so you do not have to deal with its torpedoes. You might be getting hit with Beam Overload, knocking your shields down. Then having the torpedoes hit your hull.
Do not get in too close, it uses a Photonic Shockwave that can stun you.
Only use Beam Fire At Will when it does launch Plasma Torpedoes at you.
Also remember your science ship comes with Beam Target Subsystems.
The following are the base Ensign ranked abilities. Several of these abilties are also useful when fighting against other species. That like to use tractor beams and plasma weapons. Such as Romulans/Remans, Breen, Undine and the Borg.
Polarize Hull (science)
+10% All Energy Damage resistance for 15 sec
Immunity to Tractor Beams for 15 sec
Hazzard Emitters (science)
+1,679 Hit Points over 15 sec
Removes hazard debuffs over 15 sec
+12 All Damage resistance for 15 sec
Beam Fire At Will (tactical)
Evasive Manuevers - Granted at Lt.
Toggle (7.5 max)
+X% Flight Speed strength for 8 sec
+X% Turn Rate strength for 8 sec
+15% Defense strength for 8 sec
Brace For Impact - Granted at Lt. Cmdr Rank
+33% Kinetic Damage resistance for 6 seconds.
+75% Able Crewmen resistance for 6 seconds.
There are also other abilities that are useful, regarding shield healing. Remember some abilites are dependent on power settings.
Emergency Power To Shields I (engineering)
Repairs disabled shields
300 Shield Regeneration for each facing
+15 Shield Power Setting for 30 sec
Reduces Damage to Shields by 14% for 30 sec
Science Team I (science) also counters viral matrix
450 Shield Regeneration applied once to each facing
Removes science debuffs over 5 sec
+18 Starship Operations Training for 5 sec
Consumables - Shield Battery
311 Shield Regeneration
+75 Shield Power Setting for 10 sec
Repairs disabled shields
I also find that Attack Pattern Delta is a good Lt. rank ability to have. Coupled with sensor scan, and sensor analysis debuffs. You can also consider Attack Pattern Beta.
Attack Pattern Delta I (tactical)
+12 (24) All Damage resistance for 15 sec
When receiving All Damage, applies Attack Pattern Delta I to Damage owner for 15 sec
Attack Pattern Beta I (tactical)
Grants Attack Pattern Beta I for 10 sec
to target: Applies Attack Pattern Beta I to target
-12 (24) All Damage resistance for 5 sec
-45 (90) Stealth strength for 5 sec
It's about situational awareness. You don't have to fight point blank so keep a little distance and keep an eye out for these things. They are relatively slow moving so select them with tab targeting, target the closest enemy, or click it with your mouse. Setting engine power to max and altering course also works to buyyourself some time. The can hit hard anyway but NEVER stop moving as your defense rating drops to nothing and those things can hit a nasty critical. If you are still having trouble you could try a Kinetic orPlasma resist set up but that just seems unnecessary. Brace for Impact is available for free to everyone at a certain level and that's a huge help.
Beam Fire At Will can work but it conflicts with the cooldowns on your innate sci ship's Subsystem Targeting. It also is like letting the game play for you. It makes us lazy being in easy mode during a fight. I hope some of this helps.
Depending on your level you could get Gravity Well or Tyken's Rift. If you see it launching torpedoess at you, use one of those on the warbird and it'll take out all the torpedoes.
Or you can get (once again depending on your level) Eject Warp Plasma. Stay at range and once you see it launching them at you, turn tail and lay down a smokescreen of plasma. As long as you keep the plasma between you and the torpedoess it'll toast them.
Also if the warbird does manage to catch you in it's tractor beam, you can use Jam Sensors to break it's lock and get free that way.
The big D got upgraded with 3 heavy plasma torps so you need to keep your distance otherwise you will get caught in the tractor beam and be fried.
The easy way to handle this is to take one of your beams off auto fire and hold it in reserve for torp's and mines. Yes your doing less dmg however you always have one beam ready to swat a torp out of the air.
Beam fire at will helps however you have to remember that it is random fire so it might not hit the torp in time.
As long as you keep a turret or beam on manual fire you should be fine you also need time to react to the torp or mine so stay out past 5 meters that way you have time to react to the torp.
Another useful skill your BOffs can use against mines and HY plasma torps is Tractor Beam Repulsors, which is a sci skill. This skill "pushes" any target away from your ship and can be used against multiple opponents. It also provides an "instant" kill against mines and HY plasmas.
I've found the best method for fighting these big birds is to keep my distance and stay behind them. If you are 5+km out you'll have more time to react Set energy balance to defense and focus on keeping your shields up. Emergency power to shields, reverse shield polarity, rotate shield frequency, things like that will help. Focus on taking one set of shields down then cram in as many torpedoes as you can.
The ones that really annoy me are the Romulan Escorts and their supermanouverability.
I finally defeated one of the monsters last night, thank you all for your help and suggestions.
Now, does anyone know how to pause the hints that appear at the bottom of the screen while changing locations, for example between sectors? The change too quickly (or the sector space loads too quickly) for me to read them.