I'm a bit stuck on the first one.Amazonian does fit and as Suzy says AM is short for America but although Amazonian means tough, they were not goddesses and I don't see how the rest of the clue works.
Draconian also fits and also means tough. Draconian - the Dian start and end could be a reference to the Roman goddess Diana - shortly would be the a drops off. Diana was the goddess of hunting and was associated with wild animals. But that leaves racon - the keeping part of the clue shows that it is put in between the start and end of the answer, but I'm lost with the connection between American and racon. The carnivores bit may refer to racon or it may relate to Diana being the goddess of hunting.