If you are like me, you might have started this game in easy mode just to get a hang of things and then decided to get this achievement in medium (normal) or even hard mode. To set the mode, press my adventure from the main screen and scroll down to difficulty.
You then have two choices. You can save a new game and essentially start over, but be warned, if you do that then any progress you made in the shooting galleries will also be lost as they also start over. Or you can replay the game level by level. If you do this note that there is no easy way to tell which levels you have completed in which difficulty setting from the menus. So be systematic or keep track. I ended up making the mistake of replaying some of the levels in easy mode because I didn't realize the difference. I might have restarted without a save and then the difficulty setting went back to easy so check first if you are restarting. You have to play all the levels to get the achievement.
One way that you can tell which level you are currently in is by the score you get for shooting animals. For example in easy mode you get 50 points for shooting a crow, 100 points in normal or medium mode and 150 in hard mode. But you have to be in the level to find out.
The only real difference I noticed between easy, medium and hard modes is the amount of shots it takes to kill animals and how much damage you take. I.e. you die faster . Other things like rock climbing, sledding or finding the hidden items appears to be the same in all three modes. If you are into leaderboards, you need to use a more difficult setting to get higher total scores.
If you are replaying the game, save yourself lots of time by pressing A to skip all the dialogues and cut scenes.
If you already decided to start the game from scratch in the medium difficulty setting, you can ignore this information, just play through and you'll get the achievement when you finish the last chapter.