This guide give you some useful tips to beat the mission.
How to Complete Battleships VS. Torpedo Boats Mission
First tip: Use smaller caliber guns and use a lot of them. Just put a lot of 3 inch guns on your ship and try to tay out of torpedo distance.
At super early tech, with even average crews, you need to be within 1km to hit reliably. Make sure your battleship has plenty of 3 inch guns, then just plough through them using manual rudder control to dodge the torpedoes. Turn towards the torpedoes at full rudder and you should dodge them. Make sure your ships steering, rudder, engine and fuel time are all optimised for turning. Auxiliary power also helps with turning, and pumping.
Bully the torpedo boats.
Pay attention to hit chance feedback. My problem was weight unbalanced design. 38% penalty. If you remove forward 4″ guns and play with fore/aft armor you can get it down to 8%.
And switch shells to manual HE. You also can take the veteran crew (+30% bonus to hit).
Also your towers seem to effect your chance to hit so don’t go cheap on your towers, if you want accuracy.
In addition to the advice above, this one is much easier if you keep the cost of the ship just under 50%, so you get two of them.