This achievement can be unlocked through the course of a campaign playthrough, but you’ll most likely to achieve this in the later stages of a campaign. You’ll find that most Kings and Queens of factions in Bannerlord are heavily guarded at all times, with enormous armies of their own, and similarly large armies commanded by their allies never too far away. This means that to even consider facing one of their armies, you’ll need a significant force of your own and preferably some allies in the form of commanders who can back you up.
If you don’t have many allies but you’re at a stage where your own army consists of high level troops, and you have at least 200 of them, you can begin to consider taking on the armies of Kings and Queens. In truth, you’ll fare far better with an army of 400+, but it is doable with around 200 if you’re careful. If you find a King or Queen isolated from their allies, you can always try fighting them even if you’re outnumbered, but keep in mind that you still need to find them on the battlefield. They will often use horses and stay towards the back of their army alongside other cavalry, but sometimes they’ll be foolish enough to charge you with them. If the former occurs for you, try flanking them from a position of stealth, such as a wooded area.