You will earn this achievement following the fifth story mission's completion, Rough Landing.
*** Spoiler - click to reveal ***Lara will make her way across a ravine in the Peruvian Jungle and then encounter some jaguars which she will have to fight off. You will manage to kill one, but the Empress Jaguar will cower off at this sight. Do not worry though, because after travelling further into the jungle with Jonah, you will run into the Empress Jaguar again and have to kill her once and for all.