Here's a list of all the animals you need. Some of these have challenges associated with it, but not all of them. Note that a bit later in the game you can purchase maps to find the location of all the animals 01 - 20 on the list below in Hope County. The animals in the expeditions are hard to miss.
For the monstrous animals, I recommend relogging if you can't find them. I had problems to find the monstrous Cougar. After looking for him for 5 minutes I relogged. One minute after I looked around I was hearing a fight with a cougar - went to it and sure enough there he was.
In general, the monstrous animals get into fights a lot so if you are near his spawn zone and you hear fighting nearby then you got a pretty good chance that you will find highwaymen fighting your prize already.
Also: Monstrous animals are epic enemies so don't take them on until you have a few epic weapons otherwise it will take a while to take them down.
Animals in Hope County:
Animal 01: Deer
Animal 02: Pronghorn
Animal 03: Rattlesnake (Hope County - usually near Treasure Hunt locations)
Animal 04: Wild Dog
Animal 05: Elk
Animal 06: Caribou
Animal 07: Boar
Animal 08: Wolverine
Animal 09: Wolf
Animal 10: Demon Fish
Animal 11: Bull
Animal 12: Bison
Animal 13: Moose
Animal 14: Black Bear
Animal 15: Grizzly Bear
Animal 16: Cougar
Monstrous Animals
Animal 17: Monstrous Bison
Animal 18: Monstrous Boar
Animal 19: Monstrous Bear
Animal 20: Monstrous Cougar
Animals in Expeditions:
Animal 21: Skunk (Expedition: Alcatraz - in one of the orange cells, have to shoot/punch the lock)
Animal 22: Hare (Expedition: I. S. S. Crash Site - somewhere in the woods)
Animal 23: Cattle (Expedition: H. M. S. MacCoubrey - near Lighthouse)
Animal 24: Crocodile (Selene's Recruitment Mission or Expedition Government Plane Wreck near water)
Animal 25: Shark (Expedition: H. M. S. MacCoubrey or Alcatraz (in the water - duh!)
Good luck!