When you have an option to bash a gate, door, or chest, bash it. If you select the lockpick or spell options, rather than bash, you will miss this achievement.
A few doors don't have a bash option. Don't worry, if you don't have the bash option, it's ok to open it via another means.
You do not need to go out of your way to hunt down all the gates, doors, and chests. Just use it on the ones you were going to interact with anyways.
If you've followed these instructions, the achievement will unlock immediately after