Another vote for using fill flash, which I also highly recommend in daylight hours. BTW, fill flash also produces some nice shots with shutter priority mode.
Here's a couple tips for trophy photos.
1. Position the animal so the sun is at the photographers back.
2. Remove all intervening vegetation between camera and subject.
3. The photograph should never be taken with the camera above eye level of the subject. Keep the camera low and angle the shot up wards. If you can get sky behing the horns, do it.
4. Frame the shot correctly. This kills me to even mention but I've seen so many shots where the hunter and animal look like specs in the middle of scenic landscape photo I gotta. Especially on digital cameras when it's possible to instantly review the shot there is no excuse for this.
Combine those tips and you'll be ready when you get something like this