***EDIT***
Some people are reporting that the Compy spawn is no longer infinite in the JP3 level. If you are not comfortable playing the game offline unpatched and returning online to unlock the achievement, Harley3651 has suggested an alternative:
"There is a gold brick challenge in the open area of the 1st movie where you need to kill 10 of them for the brick. If you do it 4 more times the achievement will pop"
***Original Solution***
This achievement is awarded for defeating 50 Compys across your playthroughs. The total is cumulative for player one so you can kill 20, quit out and kill 30 another time. If however you are playing in co-op, player 2 will need to kill all 50 in one session to earn the achievement.
Compys appear across multiple stages and if you are playing solo and don't let the AI get all the final blows on the compys you encounter then you will probably get this naturally over the course of your story and free-play runs.
If however you missed out on some kills to payer 2 or the AI and missed out on this, or you just wish to farm it at your earliest convenience, there is a level with an endless supply of the compy goon enemies.
In the first stage of Jurassic Park 3 "The Landing Site", at the top left of the first area behind the plane, there is an endless supply of compys that spawn from behind some barrels. Simply punch them until they get knocked out until the achievement pops. Didn't take me more than 5 - 10 minutes on my run to get this.
A bit of an extra heads up, this achievement does not track in the Xbox One Achievements app, meaning the game tracks it internally. So don't be worried if you try to check this in the Achievements app and find your progress at 0% even though you have beaten multiple compys.
(If you vote the solution down, please indicate why in the comments so I can rectify any possible issues with the guide.)