Iagoo told him to kill a famous roebuck, a deer with antlers
Identifying the most hunted animal depends on whether you mean hunted by humans or by predatory animals. Even then, sources disagree. Various sources report the deer is the most hunted animal, but some say quail, ducks, rabbits, or mice are the most hunted animals.
2,138,592 b.C.
adam
a lion
Mankind has known about (and hunted) animals since the dawn of Human time.
The first animal she drank blood from was a mountain lion... but she had tried hunting a group of elk at first; she had to stop hunting because she smelled a human nearby and did not want to kill him/her.
a bear
Hiawatha
That happened so long ago that there's no answer to be had. Since man is an animal, and Cain killed Abel (both men and animals) man may well have been the first animal killed. But like David ansered, there is no real answer that can be proven.
He wore the "hide" of the Nemean Lion that he killed as the first of his ten labors.
If you are referring to the first European immigrants to Canada, they hunted beavers. The aboriginal people who were there first, hunted all sorts of animals.
The tribe Yute mostly hunted, killed people on their land (trespassers) and ate everything that crossed their border. They were the first tribe to figure out how to make bow and arrows in the 1200's.