Very cool game and concept.
I like that the movement is a lot more controllable than before. I also like the impending auto scrolling screen of doom. It gives off a bit of panic to the player to quickly progress. I think the addition of enemies to disrupt your pathing is great as well.
I think that getting hit should give off some visual effects as it's a bit hard to notice when health is lost. The text in the corner also needs to be a bit bigger and have more contrast as it is kinda hard to see. Maybe a new feature of swinging the gun into feathers as a way to defend yourself could be neat, especially if there's too many birds and not enough lives or bullets to go around?
Overall, great improvements.