I have definitely had birds attack my quadcopters dozens of times (over about 15 years of flying).
The easy ones are actively nesting birds, like swallow, kites, and some sea birds, but they give up easily when I fly away from their nests.
The more problematic birds have been raptors, such as red-tailed hawks, bald eagles, and Ospresy, who seem to be defending their hunting territories. Sometimes they'll follow and dive bomb my drone for what feels like a very long time.
I too use the "climb" quickly technique to avoid getting hit. Raptors can dive, fly forward, and turn left or right very quickly, so trying to get out of their way by flying horizontally or descending is the least effective thing you can do. But they can't abruptly "pop up" as quickly as my drone. Indeed their attack training is based on the way that other birds can fly, so they aren't prepared to respond when the drone suddenly pops straight up. So my emergency technique is to quickly "pop up" out of the way, right as the bird is closing in on the drone, and then beeline it back to my location as fast as possible, descending gradually along the route, so that I can pop up again to avoid another incoming attack, if needed. Works best when you can clearly see the bird and the drone! ;-)
I tried using various types of tape to ward off birds years ago. It didn't work.