I have only experienced a bird targeting my Mavic once. It was in NZ and one of their giant seagulls chased me around for a good 30-45 seconds. I was hovering over a pier and the seagull was sitting on one of the posts. It took off and started squawking and climbing in a circle till it was at a similar height as the Mavic (about 30 meters). I made some evasive motions and moved away but it kept following for quite some time. I eventually decided that I'd had enough and since I couldn't reduce my altitude (as it was keeping up underneath), I popped the Mavic into sport mode full throttled up and away. He was quite fast and could somewhat keep up in land speed, but not even close in vertical speed. I reached the 120m altitude ceiling and just kept going until it gave up. I probably ended up about 500m away from my original point by the time the chase finished. It must have had a nest nearby and thought I was a hark or such after it's young.
All in all, the Mavic wasn't really in any danger, but I could see it becoming and issue it the bird was VERY determined and you reached the AGL height limits. Best best is to move into sports mode as soon as you realise what's happening, get high and far away. I'd assume most birds would only chase to protect their young.
