This score based event is seriously strange. The fastest way to progress is to take a low rank event vehicle and kill new players. As soon as you die, just exit the battle, enter next battle and repeat! This can give you a very high score/min!
In this case, 3min 27sec of Time Played, gave me 3436 score! Of course not every battle will be like this one, but your average score/min is far quickest if you use this method from all the options I tested so far.

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