**IMPORTANT NOTE BEFORE DOING THIS**
This game is known to be a little buggy. If you do not pop the achievements when they should, do not worry as the game will still register your progress and spawn the locations needed when you've met the requirements. If you need help figuring out what is still needed, you can check which Royal Arms you have as the achievements line up with the Royal Arm obtained(ie: Path of the Pious unlocks the Scepter of the Pious), by process of elimination you can see what requirements you still need to work on.
It's important to note that this achievement is NOT entirely story based. There are 7 story based Royal Arms, and 6 others that you will need to fulfill requirements for. You will need to fulfill the requirements of the following achievements before this can pop:
After completing each of the above achievements, a location will spawn on the world map that looks like a dungeon entrance. Simply select these entrances to have the respective Royal Arm added to your arsenal.
It may not be likely that all of the above will be complete by the time you finish the story, but you are able to replay chapters to work on what you may have missed. If you do manage to complete these requirements before the end of the story you should get this after earning
If there are any tips on how this solution can be improved, please let me know in the comments!