Omaha is a good cruiser. It has a decent rudder shift, turning radius, and guns pointed everywhere. Just keep turning and tape down the fire button.
AP at a battleship from a cruiser usually does next to no damage, unless you get lucky with a plunging shell hit; most bounce off the armour belt, and the others over-penetrate the superstructures. Usually only use AP on cruisers with armour that is thin enough for the shells to get through, and sometimes on carriers if the distance means the shell speed won't go right through the ship.
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