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Destroyers I still haven't figured out. They a supreme glass cannon with their torps.
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Destroyers are great acting as support ships, scouts, and ambushers.
The US ships tend to do better supporting the main fleet (because they have better AA ability and better main guns for chasing opposing destroyers away) and the Japanese ships tend to do better as ambushers (because they have better, longer range torpedoes and the ships are harder to detect).
A great tactic is hiding behind a land mass until a battleship (or even a cruiser) passes close by: pop out, fire torpedoes, pop smoke, and run away.
Torpedoing carriers is tougher at higher tiers because the carriers are pretty fast, but the fast-firing guns loaded with HE shells will still make short work of them (just stay outside their secondary range or you'll be torn apart).