Age of Empires II: Definitive Edition (PC) - Achievement - Chasing the Crown

Kill King Takayutpi before 5 minutes have elapsed in the first Bayinnaung mission "The Burmese Tigers".

This is a relatively difficult timed achievement. Five minutes is not a lot of time to track the King across the map, kill a few units along the way, destroy his Castle and then kill him.
This method is basically just to do all of the above as fast as humanly possible. There are a couple of things to note which should make this a little easier. Firstly, one of your starting heroes is basically a Monk and as you chase the King across the map, you will come across a few enemy elephants. It's important to convert as many of these as possible as you will need the damage to take out a Castle shortly as quick as possible and elephants will be able to soak up a lot of the damage too.
Secondly after you get to the initial camp where the King is and he flees, if you continue right, you will get control of a few more troops including a Monk. With this second monk, make sure to convert elephants on your way to the Kings castle as well.
The third thing to note is that the King will exit the Castle once it reaches a certain level of damage and he will make a run for it. One tip for making this easier is - As you are destroying the castle, send one fast moving unit further to the top right of the map and you will get some ranged horse-riding troops that will make it easier to snipe the King when he does leave the Castle.
Do all of the above as fast as you can and if at first you don't succeed, just keep trying to do it quicker and quicker and shave some time off. Your starting heroes are all expendable, so don't worry about losing them either.