In Cold Run, look for a narrow offshoot on the northeastern side of Hakon's Fjord. In order to get there, you must climb the snow-dusted slope just south of the offshoot and jump down into it. You can see the crazed exile's encampment from the top of the slope. As soon as you jump down, he will banish you, unlocking the achievement.
Here's a shot of my map when I landed in his area.