The Pro Adventurer 30
Finish Story Mode on the Medium difficulty setting
See "The True Adventurer."
There Is No Match For You! 30
Hunt three bears in Story Mode
Story based. There are several bears in the game, though you should get this while defending the cabin against the two attacking bears.
Cat Dominator 30
Hunt four cougars in Story Mode
Story based. Cougars are not as common in the game, but you will come across enough before finishing the game to unlock this achievement.
Hunting Holds No Secrets 30
Finish three hunts in Story Mode
This will unlock very early in the game. Any objective based kill counts toward this, so you should unlock this while gathering supplies in Chapter 2.
In Your Face 30
Hunt 15 animals using Focus Shot in Story Mode
See "Super Sight."
Off My Leg 30
Hunt three latching animals while in Story Mode or Shooting Galleries
See "Stop Chewing My Leg."
Hunting For Gold 30
Obtain gold medals in all Survival Shooting Galleries
There are 9 galleries in total, and these can be done on any difficulty. In Survival, you will keep doing laps of the map until you die and the objective is to survive for as long as possible. Since these can be done on any difficulty, change to easy difficulty in the options menu. Some of these are quite easy, though the first gallery is not one of them. Once you acquire gold on the first level, you should have the skills necessary to get through most of the rest of the Survival galleries. Tips can be found HERE
Keep Them Comin’ 30
Obtain gold medals in all Quick Draw Shooting Galleries
This is the hardest achievement in the game. Quick Draw galleries require you to get to a certain level of points, and provide you with perks and point multipliers to make it easier. The idea is to reach the maximum perk level in a certain amount of time. Unfortunately, if you get hit, you will lose the most recent perk you acquired and have to start again at the beginning of the previous perk, though you will keep your multiplier. You have very little margin for error, so you are basically going to want to not get hit at all, meaning that predators or any animal charging at the screen will always be your top priority. You will also probably need a few runthroughs to give you an idea of where the predators come from. Tips can be found HERE
The linked thread suggests playing on hard for the Quick Draw galleries, but medium may be easier. You will get fewer points, but it will also take fewer shots to kill the predators, giving you more margin for error.
The Super Semi 30
Hunt 10 animals with the semi auto rifle in Story Mode
You will unlock the semi auto rifle part way through the story. There are enough animals to get this over the course of the game, so don't worry too much about it, but don't waste too many kills by using a weapon that you already have the achievement for.
The Bolt Connoisseur 30
Hunt 30 animals with the bolt action rifle in Story Mode
You get the bolt action rifle very near the beginning of the game. There are enough animals to get this over the course of the game, so don't worry too much about it, but don't waste too many kills by using a weapon that you already have the achievement for.
The Shotgun Master 30
Hunt 20 animals with the shotgun in Story Mode
You get the shotgun partway through the game. There are enough animals to get this over the course of the game, so don't worry too much about it, but don't waste too many kills by using a weapon that you already have the achievement for.
The Handgun Sheriff 20
Hunt 20 animals with the handgun in Story Mode
Story based. You get the handgun near the beginning of the game and it is the only weapon you can use while hanging on a cliff. As a result, you will probably get this on Level 2 shooting nothing but birds. Don't bother using this against land based emenies, since they should be used to rack up kills with the other weapons.