Greek myth has at least three giant boars: Calydonian, Crommyonian, and Erymanthian. While giant boars are relatively "realistic" as it is, there's no reason to hypothesize genetically engineered giants, as we've got a real animal (or a family of animals) close enough to fit the bill: the dinohyus ("terrible pig") and the whole enteledont family.
Dinohyus was 12 ft long and 5' 1" at the shoulder. That's plenty to give Heracles a challenge!
The familiar image of the satyr of a half-goat, half-man creature is a later invention. The original conception was of a some hirsute guy with big ears, a pug nose, and a goat-like tail.
|A Hellenistic era satyr|
Last but not least are the drakones or dragons. These are almost always depicted as just as big snakes in Greek art. Not as cool as modern conceptions of dragon? Well, it was good enough for Conan! And there's titanoboa upping the ante on very real world giant serpents.