For this achievement you just need to use each of the hunter power-up abilities once.
As you go about the slaughter of the meek of the earth you will acquire special abilities.
Which ability you acquire is determined by the method you used to kill a creature.
So if you use your rifle equipped with a scope and take down a rabbit from 200 ft away you’ll receive a Laser Bullet, if you’ve done this in the first few seconds of the challenge, or after reloading you may also get a Quick Draw power up. If you shoot an animal at close range (less than 60 ft) you’ll get the Thermal Cam. Most often you’ll also get an X-ray Cam for this as well. You can only have one power up at a time so if the one listed at the top is the one you want to use, be sure to press the B button to switch to it before it expires (4 seconds). Also if you have two you can use the one at the bottom, and then quickly press B to switch to the other. This way you’ll get credit for using them both.
The X-ray Cam (icon of a deer skeleton) is going to be your best friend. While the Freeze Animal and Slow Time (which you tend to get for shooting multiple animals quickly) are great for killing multiple targets at once, you’ll need the X-ray Cam to get those 100% integrity awards.
If you just play through the game and use whichever power up is available you should easily get all seven of these achievements. These also carry over if you redo a stage, so if you want you can just start a challenge, use a particular power up and keep repeating it over and over until you have the achievement. But it will easily come through normal play without any work on your part.