EDIT: Since writing this solution I put together a complete walkthrough for the game and, as such, refined this process. Rather than repeat myself, take a look at the relevant section of the walkthrough
here.
A quick summary is to remove all feeders right away, aside from the relevant ones in a couple of enclosures where you can keep the desired dinosaurs alive. Most of the 'wild' dinosaurs will die off naturally, reducing the number you need to deal with.
I'll leave the original solution below in case anyone is interested.
This achievement remains buggy. I had a lot of trouble getting this to unlock. I came across
True_Boredom's solution which I've outlined here. Credit to them!
Proceed normally until you are:
*** Spoiler - click to reveal ***tasked with testing the new cure on the Carnotaurus. This occurs at the end of the 3rd mission on Nublar North, which is the 1st island in the dlc. Expect to take around 1.5-2 hours to get here.
I tasked rangers to do tasks automatically up to this point so that doesn't matter and won't effect the achievement.
You can go ahead and cure the Carnotaurus, then set up an enclosure with at least 5 herbivores - Sinoceratops and/or Gallimimus work well. Make sure they are fed, watered and content - you need them to survive! Including the 3 carnivores you should already have enclosed, that makes up the minimum 8 dinosaurs you need to complete the objective (although that is not stated). The infected herbivores will show a low health (32-35%) but should outlive all the other dinosaurs.
Go around the map and demolish all the feeders - there are plenty randomly spread across the area. Use the map -
- to spot them easier.
Now just wait. This might take 20-30 minutes. All the infected dinosaurs outside your enclosures will die, but it will take some time. Keep track with the objective in the bottom right. Remember to keep an eye on the enclosures to make sure they all remain content. Once the number is down to 5, being your 5 enclosed herbivores, make a save (just in case).
Go ahead and
manually cure the 5 herbivores, which
should work. After 2 attempts at running all over the map chasing 50+ dinosaurs, this was much easier and successfully unlocked the achievement!
NOTE: You will want to do this on a separate save. The dinosaurs you save on this mission that will have an effect later on - refer to John Hammond's dream for more details.I hope this helps and best of luck.