I've been flying the Atrox for a bit, great ship. This ship does two things very well, and only does these two things. The first is tanking. It can tank like no tomorrow, and can endlessly keep up against elite borg cubes. Tac cubes give it a challenge though. I personally run with a lot of double Boff skills, double tac team, for the shield distribution, double transfer shield strength, for shield regen, and double emergency power too shields, for constant 125 shield power.
The other half of this ship is a healer, and field control. Healer primary. Use double shield transfers and double hazard emitters for that, that way you can keep a constant regen for your ship going, on both hull and shields. Most tacticals will be repaired with one each, and cruisers can get 3/4 of their health back with just one hazard emitter. If you'd like, extend shields can help as well, and we shouldn't forget about science or engineering team either, but I find with double tac teams, the cool down for them can be very long.
The last part is field control. I use eject warp plasma, and gravity well, combined with danaube runabouts for field control, most times that works just fine.
Everything else can just go according to taste. A carrier isn't meant to be a frontline assault ship, leave those to the tacticals and dreadnaughts. It's meant to be a mobile hospital with fighter support. If you really want to deal more damage, I've heard peregrine fighters can be quite potent.
I am having fun with my tactical Atrox, but many people will tell you it is a bad combination.
In my experience, there are several ways to make it work, though. Personally I am fond of torpedos, which, if pointing rear, will be surprisingly easy to bring to bear against even escorts. For such a build, I use Tactical Team1 and Torpedo High Yield2 (and be sure to have porojecile weapons doffs then). Torpedoes have the advantage of allowing you to run the ship on full aux power (buffing your sci boff abilities) without costing you dps.
Obviously, you'll want at least one beam to make use of your ship's innate target subsystems abilities.
If you go for all energy weapons, you need to run high weapons power, so choosing sci powers that are not affected by aux level becomes essential - as well as having aux batteries. For such a weapon loadou, I have had much fun with a DBB fore, a beam aft and BO2 as Lt Tac power.
For Defense, I have made good experiences with Engineering Team1, Reverse Shield Polarity!, and Aux2SIF as Engineer powers, with the burden of shield healing being left to Sci powers like Transfer Shield Strength and Science Team. Many will tell you that you should use two copies of Emergency Power to Shields instead - you'll have to see how that works out for you. For me, too fewhull heals are not good. In any case, you also need at least one copy of Hazard Emitters.
As a tac, at least as the game works now, I'd recommend to add one copy of Feedback Pulse to your arsenal. Your tac buffs will increase that power's damage, which makes for some hilarious encounters with escorts and bops who blow themselves up that way. It requires full aux power or burning an aux battery for maximum effectiveness, though. Using two copies of Transfer Shield Strength and Feedback Pulse will allow you to chain those 4 powers together, so that your are never without one of them.
I personally try to avoid any deflector-based sci powers , because the Atrox is just too slow to use them much. Except for Grav Well, which may be worth it, anyway... depending on what you want to do (it works well the STF Khitomer Accord, for example, to stop the approaching Borg ?probes from reaching the Time Vortex).
As pets, many prefer runabouts for their cc and escort-stopping abilities. Personally I like Stalkers more (because they shield strip better and can disable enemy aux systems), and with season 6, maybe Advanced Delta Flyers with their transphasic torpedoes will be the fighter of choice.
Promote what you love, instead of bashing what you hate. https://youtu.be/VrJiU9BOEBI?t=53