The first thing you need to consider is what type of bird it is, there are 11 types of Birds of prey but not sure how you could believably win against any of them
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It's a giant four-winged bird demon, does that help with classification?
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They'd have a better chance against a regular bird! You'd have to limit the birds'abilities to kill them easily. I'd say possibly a dense part of the forest that way it can't just swoop down for an instant k.o. Causing something to fall down and pin the bird temporarily would be the only plausible way I can think of as of the moment. But to figure that is up to you my writer friend.
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Drop something from above, eh? Darn it, where's a coyote when you need one?!
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Nah he fares badly against birds