Realms of Arkania: Blade of Destiny

I'm not entirely sure just how many caves happen to have rats, but there is one that for sure does, and the rat hole is right through the entrance. You want to travel to the city Runinshavn, located on a small island at the bottom-center of the map.

Once you're there, you need to travel down towards the lighthouse. When asked which path to take, take the center one. Soon after, you should run into a cave with steps leading into a dark cavern. Enter it.

On the left-hand wall is a rat hole. Approach it, and then select the prompt to reach your hand inside. The rat will bite, and then the achievement will unlock.