For this achievement, you’ll have to raise a Monster’s ecosystem rank to S.
To do this, you must release multiple of the same monster into the wild from your stables. To release a Monstie, select the Manage Monstie option on one you want to release. You’ll have 2 options: to Change Name and to Release Monstie.
To check your progress, head to any of your established camps and select the Habitat Restoration option. Having this option available may require a little progress through the main story until you help out with a Rathian.
Highlight an Area, i.e. Sunpetal Plains, and you can see the Ecosystem Rank bar chart in the bottom right. Once you get one Monster to S rank, the achievement is yours!