The chupacabra can only be lured (using three goats) on your second visit to Puerto Rico. On the first, you have to get the fur from the barbed wire at the herder's brother's ranch (star at the right on the Jeep map) and take it back for analysis.
When you return, the herder is planning to trap the chupacabra. His brother suggests that you use the jeep to chase three spotted goats into the clearing at Snaggletooth Rock (center star). The chupacabra will come after them if you succeed. When all three are in the grass circle, get out of the jeep and join the herder.
Not really
Yes, you can find proof of The Jersey Devil, Bigfoot, Nessie, and the Chupacabra. (see related question)
You can't. But its tooth is proof enough that it is an unknown species.
Take it back to Mews. Once you have gotten the photo of the Yeti footprint, and proved the other three cryptids (Nessie, chupacabra, and the Jersey Devil), Mews will send you to track down Bigfoot.
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.
You have to look for Bigfoot/Yeti in the Himalayas, the Jersey Devil in New Jersey, the Loch Ness Monster in the Loch Ness in Scotland and the Chupacabra in Puerto Rico.
You need a photo of Nessie at Loch Ness, a tooth from the Chupacabra from Puerto Rico, and egg shells from the nest of the Jersey Devil in New Jersey. (see related solution)
When you first start the island and you get the paper about Mews needing the evidence of ONE cryptid to get your reward, you end up needing to search for 4: Bigfoot, the Loch Ness Monster, the Chupacabra, and the Jersey Devil.
you have to have three goats and.. that farmer dude to help you
After you have confirmed the other three cryptids (Nessie, Chupacabra, and the Jersey Devil), and brought back the inconclusive footprint from the Himalayas, Mews will send you in pursuit of Bigfoot, which is similar to the Yeti.
The chupacabra can only be lured (using three goats) on your second visit to Puerto Rico. On the first, you have to get the fur from the barbed wire at the herder's brother's chicken farm (star at the right on the jeep map) and take it back for analysis. When you return, the herder is planning to trap the chupacabra. His brother suggests that you use the jeep to chase three spotted goats into the clearing at Snaggletooth Rock (center star). The chupacabra will come after them if you succeed. When all three are in the grass circle, get out of the jeep and join the herder.
The three spotted goats at Snaggletooth Rock (center star) are going to be bait for the chupacabra. On your first trip to Puerto Rico, get the fur from the fence at the chicken farm and take it back to the mews lab for DNA testing. When you return to Puerto Rico, the goat herder is setting a trap for the chupacabra at Snaggletooth Rock. Use the jeep to chase three spotted goats into the grassy area there, then join the herder to wait for the chupacabra.