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Hey Lunchcutter,
As other captains have pointed out, when you are in a BB like the NM and you are aiming at a Kongo, make sure you are aiming at the waterline with AP. Let us talk about the New Mexico first, she is a "shotgun" style BB just the her IJN counterpart the Fuso. Accuracy wise she is not the best but you do your damage with volume of shells. I have played many battles in BBs so lets see if I can give you helpful tips =).
Tips:
First and foremost you will be shooting AP the majority of the time in BBs. Yes, there are cases where you will shoot HE (shooting at a bow on Yamato) but for the most part you will shoot AP and do good damage. We did recently change the amount of damage that AP does to destroyers (with a couple exceptions) to the equivalent of an overpen (10% of shell damage). I almost always shoot AP at all destroyers even after the change due to the guaranteed damage you get, HE is ok if you have time to switch to but BBs have long reloads even with expert loader captain skill. The other downside to HE is you sometimes will just knock out/destroy modules and not do any damage to the enemy ship. This of course is something you will learn over time in BBs.
When you are aiming at a broadside of any ship, aim for the waterline. That is where you will be able to do the most damage with your AP shells, just remember that angling is a thing (I will be covering that in my tips post in the near future).
Prioritize targets, as a BB player I will look for the squishy cruiser first and then the enemy BBs. You will also want to shoot at DDs, I see players say I can't hit a dd (you will never learn how if you never shoot at them. =).
Last but not least practice! There will be times you have the perfect shot lined up and oof RNG says no but the more you practice in BBs the more comfortable you will become!
I hope these help and I am sure other captains will have more tips/tricks to using BBs well!