For the US Super battleship mission, I built a 9 x 18" ship, super heavy shells, best long range rangefinder with 16" belt and 6" deck, 30 kt speed. I kept the distance so most of the the escort did not attack me.
Try to pummel the BB with best accuracy first, you do not need to kill him immediately, just damage him enough so his accuracy drop to ~ 1-2% and switch to other BB. That will keep your BB in good shape so your accuracy penalty does not scale too much. When those BBs cannot hit anymore , you can try to slow down to your cruise speed to maximize accuracy and to conserve the ammo.
My only problem of this mission was ammo capacity. I won this mission with ~ 20 main gun shells left because 1 of the 3 BBs took 141 x 18" shells to sink (my accuracy is about 20% most of the time).
For Prove Your Might mission tips, you can view this post.
Personally, I think Prove your might and Contest in the Black Sea are the 2 most difficult ones because you need to play a certain way to win.
Some tips for Contest in the Black Sea mission:
- Head southwest, keep your BC and CA close to your DDs to get bonus spotting from them.
- In the early minutes, spam 22,5 km range torps to slow down their BB and BC and strip those 20 chasing DDs of their BB and BC bonus spotting while your group run as far as you can from their capital ships. This is very important because without bonus spotting, those enemy DDs cannot spam torps from afar which can be very deadly.
- After about 1h of running away with spamming torps to your back, your battle group can try to slow down (I used 22 -26 kt speed), let some enemy DDs to catch up and focus fire them to death. Rinse and repeat until you win