The proof is at each of the locations, but there is some less-than-convincing evidence. You get a photo of Nessie at Loch Ness that is faked, and another one that is a movie prop. But you finally get a real photo.
You find some fur on your first visit to Puerto Rico that turns out to be coyote fur, but you return to trap the chupacabra.
You find a footprint in the snow in the Himalayas that is unconvincing, but when the three other cryptids are proven, you get to hunt for Bigfoot instead.
first you have to find all the other cryptids then you go in the helicoptor to the new location and follow him to his cave
You could get all you want because you actually have the whole creature at the end, before he is evidently released back into the wilderness.
It means that there is scientific evidence that the cryptid exists, which is what you are trying to do for the 4 unproven cryptids. When all are confirmed except the Yeti (and you have the footprint photo), Mews will send you in pursuit of Bigfoot, who is soon confirmed.
After you watch all 5 videos in the Cryptids Museum, Mews will return and give you some more instructions. Then you can fly off to locations in the helicopter.
Find all 4 cryptids
When you have reviewed all 5 videos in the museum, Mews will arrive, show you the lab, and ask you to hunt down the cryptids.
The heliport at Mews' house is out the door, then to your right. You cannot use the helicopter until you have reviewed all of the videos on cryptids and spoken to Mews.
Go to the museum (first floor right) and watch all 5 of the cryptids videos (at least part of each one).
After Mews leaves the bedroom, drink the water and go downstairs to the room on the right, which is the cryptids museum. Look at all 5 videos there (at least part of each one) and then Mews will appear to offer you the chance to track down four of the cryptids.
Watch all the myth videos and let the guy brief you on the mission.
There was no way to see the actual monster on the Cryptids Island preview. Likewise, there is no way to see Nessie with the telescope in the actual quest. All you see is items disappearing into the water. (see related question)
You will search for evidence in four locations around the globe where cryptids have been observed. Ask you discover possible clues, you examine them to see if they are genuine. Nessie - at Loch Ness Yeti - in the Himalayas Chupacabra - in Puerto Rico Jersey Devil - in New Jersey You will be able to prove all but the Yeti. Only when you prove them, and have the unusable footprint photo from the Himalayas, will Mews send you in pursuit of Bigfoot in the Pacific Northwest.