This isn't a particularly DIFFICULT achievement, although it is a bit time consuming.
First, get a 5 star Park on the beginning island to unlock Sandbox mode on Isla Nublar. It also helps if you've researched the Indominous Rex and/or the Indoraptor, as they have a high base rating.
Set up the sandbox with infinite funds, no failed incubations, no breakouts, and high chance of dinosaur fights. Then set up say 10 hatcherys (or more, but 10 is good enough) in a relatively small enclosure. Then just start pumping out modified mutant dinosaurs. I find Bone Density to do the most for rating.
As a dinosaur kills another, it inherits 50% of its victims rating. Keep producing high rating dinosaurs in this "death pit" and eventually one will reach 5000. You can speed things along by using a ranger jeep to heal the most successful dinosaur between its fights.