The Conquest is an interesting ship, but its weak armor and inefficient shields mean that you have to get it just right--and then it'll pack a huge punch--but if not, you could wind up losing half your hull integrity.
The Last Hurrah is a good testament to that. Oftentimes, I lose that mission after a single mistake takes me too close to a pair of Dominators, or to the Onslaught. Other times, I can utterly crush the enemy while taking minimal damage to the hull.
I think the Conquest's main flaws are
1.- Incompetent AI, as of 0.52.1
2.- Insufficient passive flux venting (requiring heavy investment in vents)
3.- Reliance on large battery of energy PD (coupled with #2, that's not good)
Of course, there's the inherent relatively weak hull, but that goes with being a battlecruiser. To remedy this, I usually pilot Conquests myself. I use a custom loadout that is usually big-gun only, with no PD. For The Last Hurrah, I use a loadout with 2x Gauss Cannon, 2x HVD on each side, with no missiles.
The rest of the points go to hull mods and vents to boost maneuverability, increase range, increase ammo, and boost flux venting. A very effective fleet capital ship, as long as it has some PD support and explosive-damage companions.
With my custom Dominator, I can take down a stock AI Conquest while taking no hull or armor damage whatsoever. But that doesn't mean all too much.