Make sure to not get hit as it is a 1-hit kill without having less than 100 health, or if it stomps on you, resulting in a respawn and the creature regains all its health, too (after the first patch). Fighting the creature near the home base helps as creatures will attack it also, helping speed up the process.

Having level 5 Spit and firing at the epic creature while walking backwards in a circle works extremely well as long as you stay out of striking range.

But this method is dubious as another creature could easily kill it.

Another method is to kill an epic is to lure it to your nest, as all of the creatures in your nest will attack it.

Do not turn your back to the Epic through this process, as it may get over due to a glitch or run away. The Epic is unable to climb the hill, but will continue to struggle to do so as long as it remains on-screen. Once on the ridge, continue to Spit at the Epic, replenishing your Hunger Meter with fruit whenever needed. The ridge should be taller than the Epic, and should have a close-to-vertical drop below. Jump (or Glide) to a flat ridge on the hill with a fruit-bearing plant. Spit to lure the Epic toward a rugged hill or mountain. Even the steepest hills can be climbed with only level 1 jump and wings, although a high jump makes things a lot easier and is recommended.).

The easiest, fastest, least skill-required way to kill a flightless epic creature and earn this achievement is to be an Omnivore/Herbivore with high (L.4+) Spit and Jump (A high level of jump is not required.

Note that the Epic had already lost over half of its health, and the creature is still starving. Killing an epic using the methods mentioned on this page, but with a carnivore.

Spore epic creature mod