By stating monstrous animals, am certain you're referring to those gigantic animals like the dinosaurs and mammoths. If that's the case, there's no record of such animals existing in our present times. The majority of them died from natural causes like the dinosaurs who got wiped by asteroids impacting the earth some 65 million years ago. Others like the mammoths got extinct mostly as they were hunted by early humans. While the rest probably got extinct by evolution itself. Don't ask me what led to the extinction of dragons, i highly doubt they even existed in the first place.
Today, the closest thing we have to a monstrous like animal are jungle cats and probably the grizzly and polar bears. I chose to call them monstrous like because they are very dangerous animals who can almost not live with humans in the same place without the fear of danger. If they are other animals asides this which can measure up to the definition of montrousity, then I haven't heard of them.