Preferably, do this achievement after having first done the Monolith Moment achievement (finding the big monolith in the snow biome). The snowy passage is very close to the monolith and you can do both of these achievements fairly quickly one after the other. Head north west from the monolith onto the rocky outcrops between the monolith and the edge of the world. The passage is a short tunnel made of large boulders and does not resemble the achievement image. I ran along the top of the rocky outcrop and was able to find the passge easily enough by doing that. The area you need to search is thankfully, not very large.
I found that personally it was easiest for me to go to the end of the outcrop at the edge of the rainy biome and climb up onto it from there, then run south along the rocks. It was very easy to spot the passge approaching it from the north.