Dragon's Dogma 2

This achievement is not missable, and can be done at any point in the game.

Location: Checkpoint Rest Town (Take the West Oxcart from Vernworth)
This achievement takes place in Checkpoint Rest Town which you will naturally come to as you make progress through the game. You may have acquired the Gate Entry Permit, Battahal Residence Permit, or Beastren Border Entry Permit which would allow you through the gate if presented to the guard. If you possess these items, you MUST store them at the inn, so that you do not possess them as you cross for this to work. Otherwise, the game does not see these as an illicit crossing.

Once in Checkpoint Rest Town, you will want it to be morning by resting at the inn or calling for an oxcart. Once morning, sit on the bench under the inn and doze off once to force the time to change to afternoon. Get up, and run north across the bridge to find an oxcart with covered car in the back heading into town. Step into this oxcart and wait about 5 minutes for it to go to the border crossing and be allowed through in order to gain this.

If it doesn't work, try again the next day.

There is an extremely easy way to do this achievement if you already have a form of passage, show it to them and open the gate and once you are in the middle of the passage, simply drop your permit(s) and then run through the gates and you unlock the achievement.
No need to do any of this cart stuff or dragging a monster, just drop the permits and run through and pick them back up once you get the achievement.

The border is located at Checkpoint Rest Town where you can take the oxcart from Verworth to get there. But the guard in front of the gate requires you to have a permit to pass, so you can just wait there for a moment till an oxcart passes by, just hide in the cart and once the cart has passed the gate, the achievement should pop. BTW, this achievement should be unlocked at the same time.

This appears to be missable If you don't do this the first time you cross the border the achievement won't unlock.

The main storyline will eventually bring you to the Rest Checkpoint town near the border where you need to acquire the proper documents to cross. Don't do this and instead wait for an oxcart heading towards the border and hop in the back and wait for it to cross and you should get both crossing the border achievements.