There are several goat herders and farmers at Puerto Rico on Cryptids Island.
The first one is where you arrive, and he loans you his Jeep to look around. The second is his brother (the chicken farmer) at the first star on the map. He thinks a chupacabra has attacked his chickens, and there is indeed fur left on the barbed wire fence. There are two other herders. There is one at upper left who has his goats in his house. You can find his bolt cutters if you climb the pegs at right. The one at lower left has his goats in a huge stack, and gives you a clue about the chupacabra.
The fur, however, proves to be from a coyote.
On your second trip, the herder prepares a trap for the chupacabra. Drive your jeep to corral 3 spotted goats into the area of Snaggletooth Rock (center star on the map). Then get out and join the herder there.
You go to the center star in the center there you will meet the farmer who will help you
The goat herder who loans you his jeep is out to catch the chupacabra when you visit Puerto Rico the second time (the first time you took back the fur sample). His brother, the chicken farmer, suggests that you herd three spotted goats into the rocks at Snaggletooth Rock (center star) to serve as bait. Once you do, meet the herder there who has set up the trap.
The goat herder is the one who makes the trap, on your second trip to Puerto Rico (the first time all you find is dog fur). Use the jeep to corral 3 spotted goats into the area around Snaggletooth Rock (center star), then join the herder there.
You can copy the women or the goat herder using the Costumizer.
On your second trip to Puerto Rico (the first time you get the fur), drive the jeep to herd 3 spotted goats into the place the chupacabra was spotted, the rocks at the center star. Then get out and meet the farmer, who has prepared a trap.
There are lots of goats at Puerto Rico, but no mountain goats.
Goat herder
At the herder's brother's house (right side star), there is fur on the fence at the chicken coop. You simply take it.
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The only trap on the island is provided by the goat herder at Puerto Rico. You can help him try to trap the chupacabra. On your first trip to Puerto Rico, get the fur from the chicken farm fence (right side star). When you analyze the DNA, it is not from a chupacabra. Go back to Puerto Rico, where the herder is preparing the trap. His brother suggests that you use the jeep to herd three spotted goats into the grass at Snaggletooth Rock (center star). The chupacabra will be lured there by the goats. Drive there, get the three goats into the rock, and then get out and see the herder.
In Puerto Rico, the goat herder's brother has a chicken farm, at the right hand star on the jeep map. There is some fur on the barbed wire fence. Collect it and analyze the DNA at the Mews lab. (Unfortunately it is from a coyote. Return to Puerto Rico and talk to the herder and his brother. You can help catch the chupacabra at Snaggletooth Rock - center star on the map.)
Any snake you can climb on is not likely to eat a goat. The snakes,gulls, and even the giant iguana are all harmless.