Successfully complete one of the following tasks to get a trophy:

Easy As Falling Off A Log (Bronze): Survive the log balance event.
I Walk The Line (Bronze): Cross all the log balance events.
I Immediately Regret This Decision (Bronze): Escape the Bear pit.
Silent Hunter (Bronze): Shoot any animal with a crossbow.
What Big Teeth You Have (Bronze): Survive a predator hunt.
F+ (Bronze): Complete any objective without getting a medal.
Searching For Meaning (Bronze): Used a scope 42 times.
Duck And Cover (Bronze): Collect all the Cover Points in any hunt.
Bronze Beauty (Bronze): Get your first Bronze Medal.
Cool Silver (Bronze): Get your first Silver Medal.
Solid Gold (Bronze): Get your first Gold Medal.
Goldilocks' Revenge (Bronze): Bag all 4 bears in the game.
Wasically Wabbits (Bronze): Shoot 20 rabbits.
One Shot, Two Kills (Silver): Shoot 2 animals with one shotgun shot.
Heartbreaker (Silver): Perform 14 heart shots.
Metal Deer Solid (Silver): Bag any deer from within 9 yards.
Splinter Smell (Silver): Get within 6 yards of any animal without alerting it.
William Tell (Silver): Hunt 30 animals with a crossbow.
Muzzlelover (Silver): Hunt 30 animals with a muzzleloader.
Pistolero! (Silver): Hunt 30 animals with a pistol.
It’s A Long Shot (Gold): Bag an animal from beyond 80 yards.
Welcome To The Order (Gold): Complete the game.
I Love Gooold! (Gold): Get all Gold Medals in any level.
A True Hunter's Sense (Gold): Complete any level without using Hunter Sense.
Ultimate Hunter (Gold): Get all Gold Medals for all hunts.
Ultimate Tracker (Gold): Collect at least 90 animal signs.
Platinum Trophy (Platinum): Get all trophies.

Additionally, there is one secret trophy:

Secret trophy (Unknown): Unknown.