Evolve

[Edit]: While servers are closing on September 3, 2018, this achievement will more than likely not be affected (although the official statement is a bit vague).

How do I get the most wildlife into a game?
To get the most wildlife in a game, you will need to start a custom game and turn on the Map Effect "Canyon Striders"

This effect is only available in the following game modes and maps
In Extras set the Wildlife Population to High and Difficulty to favor you.

Whether you play as a monster or hunter does not matter, but playing as a monster means you won't have your team attacking the wildlife and stealing kills.

[Edit]
I'm actually unsure whether a teammate can steal a kill or if damaging a creature, without getting the final blow, is acceptable, but I suggest playing as the monster with the smell range perk, as that allows you to see creatures and hunters through walls. I would also suggest playing on nest since the AI hunters will focus on the eggs instead of the monster.

What monsters are good for this achievement?
I chose Wraith. Her (the game refers to the Wraith as her) Warp Blast can kill multiple targets in a group and her abduction can snag a creature trying to run. She is locked until you get both of the other monster's past tier 1 (or buy her), but she is available with the base game (not a DLC monster).

Failure Online's comment:
Personally made good progress with just the Goliath. Upgrade fire breath to level three and that gets you some serious range. Grab the cooldown reduction perk so you can use it more often.

A quick way of getting this is to create a custom game. In map effect turn on canyon striders. And in extras change wildlife population to high. These settings will enable the most wildlife and make it a breeze as the monster.

An easy way of getting kills without being the monster is to use Markov. Markov's electric gun kills quick and chains hits. It is also a quick way of spotting wildlife if you just run around revving the gun.