Little Kitty, Big City

Very first cat you meet tells you how to capture birds a piece of bread is on the ground. Pounce on required amount of birds to get the achievement. You can also get the pounce on flying bird achievement by jumping on the bird before it lands

In order to pounce on a bird, you will need to approach it while stalking with LB while not directly in front of it. You can then hold A to aim your jump directly on the bird. There is a quest early in the story that teaches you how to get a piece of bread/bagel from a pedestrian and drop it to attract birds. While this makes it easy to attract a bird to a specific location, using food as bait is not necessary to successfully pounce on a bird. You can pounce on any bird resting on the ground so long as you get close enough to jump on it.

On the southern portion of the map is a shop where you will get a quest to pounce on a yellow bird. (There is a lizard drawing on the map in this area, you can access this region after the crow gives you a fish so you can climb ivy.) Outside of the shop at a T intersection of roads, the yellow bird and various blue birds will consistently land on the road in a few spots for a handful of seconds. If you stalk this area, you can rack up 20 birds without having to deal with getting food to bait them. Took me about 10 mins from this location as random birds will land in the same 5 spots. You can go to the center and stalk from there.