Question: The carnifowl is a bird of a unique shape

It is about 50cm long, with a wingspan of 110cm and legs only 5cm long. Its front half (chest, wings, beak) is like an eagle, though the head is feline and has cat eyes and ears. Its rear half (abdomen, tail, legs) is mostly like a turkey. However, it has paws like a dog, which have long aquiline claws. It is a carnivore, with a similar diet to an eagle. It is capable of flight

How would such a bird realistically hunt/catch its prey?

Answer: 
**It'll die of natural selection**

Don't get me wrong, I'm all for crazy creatures, but this is far, *far* too much. Eagles are slim and aerodynamic, turkeys are infamously round and bulky-like. Mashing their front and back halves together will ensure the weight of the creature, and therefore gravity's pull, will center in the *back* of the creature. That's why we don't see pear-shaped birds IRL; because their enlarged rear end is like dead weight, dragging down the poor creature.

The cat head, being bigger and heavier than a bird's, will offset this only slightly, and it's weird for a bird to have a feline head, so this doesn't help your creature either.

Your short legs, as The Square-Cube Law pointed out, are basically useless, but so are your feet. You see, having had dogs *and* cats in the house, I noticed the dog's claws were blunt, while the cat's were sharp. This is why cats have retractable claws; because constant wear and tear blunts claws, making them almost useless as weapons.

Finally, short legs and long claws? There is no way that could ever work in real life, or (IMHO) even in fiction. It's so obviously impractical no one will suspend disbelief.

**I love the name, and the idea of an new kind of predatory fowl made with parts of other animals, but your current iteration is unviable and should be replaced with something else. If I may, I'd suggest researching what makes eagles and big cats such good predators, and then put those together in a way that complements them.**
**Like an Owl.**

The body shape you described is basically the same as an owl. The cat-like head and ears also give some resemblance to eared-owls. However you described its body as eagle like, which leads me to believe it doesn’t have sound dampening feathers reducing its overall stealth. Conversely the toe pads on its paws might serve the same role as in cats: hiding the sound of its footsteps. Which isn’t considerably useful considering it has short legs and doesn’t exactly hunt on foot.

It’s cat ears give it hearing comparable to an ordinary owl, with the key difference that they can be rotated in opposite directions. Definitely a nocturnal ambush predator.