When Doing the security missions on the first island, you will have to build an ACU center. When it's built, press A on it and select the helicopter and take control of it. Then just fly towards any dinosaur and press Y to change to the dart rifle. Then just shoot a dinosaur until it falls asleep. I shot the Triceratops and it took 3 shots to tranq it. Smaller dinosaurs take fewer hits.
After the 2nd shot, the dinosaur started running. If you tranq a dinosaur while it is running, you will also get this achievement:
You can also shoot from a distance and get this achievement:
While you are at it, shoot a dinosaur in the head for this achievement: