Dragon's Dogma 2

During your travel to the castle, you can ride oxcart, but this trophy will not pop during this event. After arriving in Vernworth go to North Gate, you will be greeted by an NPC requesting help. During this side quest you will be guided how to use Oxcart, one of fast travel option in the game. Pay the oxcart guide and when you arrive in your destination the trophy should pop.

Here's a video guide to get One Speed Only achievement.