Dire Caragors are extremely powerful and extremely angry versions of Caragors.
If you see a Caragor with a big trio of lines above it (bigger than other caragors) that will be a dire caragor. And they are more **White.**
They are not often found on their own, preferring to hunt or rest with lesser Caragors in the fields of Mordor.
You can find these groups in the wilderness areas in the Sea of Nurnen, farther away from strongholds and settlements.
Alternatively, if you attempt the Graug challenge during The Great White Graug mission, you will end the mission on the back of a Dire Caragor, which you can simply kill to complete this challenge as well.
You can also unlock the Shadow Mount ability to use Shadow Strike to instantly mount the Caragor, and kill it with little hassle.
For more help in the Hunting Challenges visit this guide.