Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Easy As Falling Off A Log (10 points): Survive the log balance event.
I Walk The Line (10 points): Cross all the log balance events.
I Regret This Decision (10 points): Escape the Bear pit.
Silent Hunter (5 points): Shoot any animal with a crossbow.
What Big Teeth You Have (10 points): Survive a predator hunt.
F+ (5 points): Complete any objective without getting a medal.
Searching For Meaning (5 points): Use a scope 42 times.
Duck And Cover (10 points): Collect all the Cover Points in any hunt.
Bronze Beauty (10 points): Get your first Bronze Medal.
Cool Silver (10 points): Get your first Silver Medal.
Solid Gold (10 points): Get your first Gold Medal.
Goldilocks' Revenge (10 points): Bag all 4 bears in the game.
Wasically Wabbits (10 points): Shoot 20 rabbits.
One Shot, Two Kills (20 points): Shoot 2 animals with one shotgun shot.
Heartbreaker (20 points): Perform 14 heart shots.
Metal Deer Solid (20 points): Bag any deer from within 9 yards.
Splinter Smell (20 points): Get within 6 yards of any animal without alerting it.
It's A Long Shot (50 points): Bag an animal from beyond 80 yards.
William Tell (30 points): Hunt 30 animals with a crossbow.
Muzzlelover (30 points): Hunt 30 animals with a muzzleloader.
Pistolero! (30 points): Hunt 30 animals with a pistol.
Welcome To The Order (100 points): Complete the game.
I Love Gooold! (100 points): Get all Gold Medals in any level.
A True Hunter's Sense (100 points): Complete any level without using Hunter Sense.
Ultimate Hunter (200 points): Get all Gold Medals for all hunts.
Ultimate Tracker (160 points): Collect at least 90 animal signs.

Additionally, there is one secret achievement:

What's This Button Do? (5 points): Pressed the Left Bumper 10 times.