The main issue of a real snallygaster is the half-bird/half-reptile thing. Any animal like that would be long dead once humans came, and likely too unlike the snallygaster for the realms of plausibility
However, the world is full of tiny distant branches on the tree of life, and evolution can be a powerful thing, so let's continue
Firstly, we need an ancestor: To best fulfill the snallygaster, we'd ideally get something primitive with pennaceous feathers. Unfortunately, pennaceous feathers are restricted to the maniraptors, with true flight feathers themselves even more limited in scope. Taking this into account, we can make the snallygaster as a small primitive oviraptor, with wings and beak, but a long tail and teeth as well
This oviraptor is still far from the snallygaster, and there's a mass extinction heading its way. We could make progress with both issues if this species were to adapt to arboreal life. This would give us many changes useful to our ends; It could likely gain grasping feet and wings, and perhaps even become flighted. All these traits would bring it one step closer to the snallygaster
Being smaller, this species could likely survive the mass extinction just as well as the various avian clades. However, like all animals, it will need to change first. Firstly, it will likely have to lose its arboreal adaptations for the lack of trees (while their were some trees, they were rare and ground-dwellers often had the advantage). Given that all their limbs were in use in the trees, it seems reasonable that the same would stay true on the surface
These terrestrial creatures would benefit from some protection, both from the rough ground and from predators. Scales would be quite useful to this end. One plausible arrangement could be having the head, chest, and wings be feathered for aerodynamics, with the feet, legs, and tail being scaly to maximize protection. This would make these proto-snallygasters much more reptilian
After the extinction, there would be many niches to fill, especially for fliers. A good niche for this proto-snallygaster would be a piscivore. This would motivate adaptations like a long beak and sharp teeth, like a snallygaster. These piscivores, given the right environment, could become rather large. This shouldn't be an obstacle to flight: Argentavis, a flighted bird, was heavier than a human being
Piscivores need not subsist solely on fish. They would likely add other foods to their diet, if possible. Perhaps these snallygasters (or at least some of them) could take on a more eagle-like lifestyle, to supplement their diet if there aren't enough fish. While they won't be able to pick up human-sized beasts, small children and other similar-sized creatures would be more than light enough
They will need some way to hold their prey, however, as unlike birds they would only have 3 forward-facing toes. They could grasp small prey between the hindfeet, but they will need a better solution. One such possibility could be a large hooked claw like that of the dromaeosaurs, which could be turned out like a thumb to grab prey
Now we have made quite a snallygaster, but there are still some obstacles to the complete picture. Some traits could be considered as display; Reflective colouration could account for the metallic beak and steely claws, and a locomotive-like whistle could be an effective mating call. However, the other remaining traits are hard to justify
Tentacles, especially those of the octopus, are full-fledged limbs, which would be hard to add to such an advanced tetrapod. We can still do something similar, though
While reptiles and birds do not have cartilages on their face, it isn't totally implausible for the snallygaster to have them. A set of cartilaginous display nubs around the mouth would be a good origin for tentacles. These nubs could likely extend out as a Fisherian runaway, forming long flexible structures that would seem remarkably close to tentacles
The central eye would be another issue. Cyclopia, while it has the desired effect, is always accompanied by many other deleterious features. However eyespots (or fake eyes) are very common in nature
A single scaly eyespot in the forehead would be a useful feature, as it would resist attacks more than a feather eyespot, and it is where attackers would expect an eye. This could adapt into a large, shell-like eye-dome in the centre of the forehead
Finally, we must discuss its hematophagy. A large animal like the snallygaster could not subsist on blood alone, but other animals can
If the snallygasters are capable of withstanding hematophagous worms and bugs (which shouldn't be implausible with their thick skin and scales), then they could use these bugs as a defense, going to dense areas and even cultivating their numbers. This would inevitably result in any meat they store ending up wholly drained of blood before they go to eat it. This won't be much of a downside for the snallygaster, as there are still a lot of nutrients left over, as our own diets can attest
Overall, these changes would lead to an animal very much like the snallygaster of folklore