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Yes, those twin planes are a pain to take out, but the real death knell comes from the heavily armored boats on round 3. Your game essentially ends after your first life is lost on this round because you won't even be able to defend yourself without full firepower. One of my all-time favorite games, Darius, also suffers from this. While I have cleared the game before, I had to do it on a single life, because once you die, the game is essentially over.
The helicopter is definitely the best choice because you can 'waggle' in place and spread fire over about half the screen.