Collect the fur from the fence at the farm of the herder's brother (right side star) at Puerto Rico. Take it back to show to Mews. Follow the steps on the DNA testing carefully. Unfortunately, the fur is from a coyote. Go back to Puerto Rico, where the herder is going after the chupacabra himself.
You find it caught on the fence of the farmer's brother.
You get the fur from a fence in Puerto Rico. Back at the lab, you run a DNA test, but it turns out to be ordinary coyote fur.
At the herder's brother's house (right side star), there is fur on the fence at the chicken coop. You simply take it.
You don't. The only fur is the possible chupacabra fur on the fence at Puerto Rico. All you get from your trip to the Himalayas is a lantern and a photo of a footprint in the snow.
Run the fur through the DNA analysis, but you find that it is only coyote fur. You will have to go back to Puerto Rico to find more evidence.
In Puerto Rico, deliver some feed to the farmer's brother (right side star). There is some fur on the fence at the chicken coop.
There do not appear to be any sheep anywhere on Cryptids Island. There are many goats at the Puerto Rico location, and part of the plan to catch the chupacabra involves using them as bait. After first testing the fur from the barbed wire fence, return to Puerto Rico to use the jeep to corral the three spotted goats at Snaggletooth Rock.
On your first trip to Puerto Rico, drive the jeep to the other locations. At the upper left, there are Bolt Cutters on the top of the hill. At the right side star, the brother's farm, he says some fur on his fence may be from the chupacabra. Take the fur back to Mews for testing.
On your first trip to Puerto Rico, drive the jeep to the house of the herder's brother (right side star). He says some fur on the fence is from the chupacabra. Take it back to run a DNA test, but it turns out to be from a wild dog.
During the DNA testing on Cryptids Island, you will add the sample (fur or egg shells) to a beaker, then before add an enzyme (the red #3). Before putting this mixture into the tray, you add Lab Gel, which is yellow in color, to the tray. When you add the orange sample beaker, the tray also turns orange.
Assuming you make no errors, it is almost immediate. You may be omitting the final step, which was placed on the second page: press the flashing "develop" button on the developer.
Drive the jeep to the herder's brother's farm (right side star on the map). The fur is on the fence to the left of the chicken coop. (Although you also need the bolt cutters from the upper left star, you must eventually take the fur back for DNA testing before you can finish Puerto Rico.)