Simply complete all the hunting requests (you can start this series by picking up the paper inside Mail Offices (i got mine from saint denis but there are i think 5 other locations you can get it aswell))
after completing all the goals you'll get an invitation to the old lady and this is where you get the squirrel statue, afterwards head to your ,,Home,, (Ranch) and put the Statue ontop of the chimney, Abigail won't like it though and hide it multiple times whereas you have to find it all the times and put it back, after finding it the sixth time (ontop of a mountain lol) you will be awarded with the trophy.
I used this handy guide that will give you good tips and locations for the hunting part and also shows the places where abigail hides the squirrel:
Good Luck Cowboys