In order to obtain this achievement you are going to want to start off by creating a new world with the following settings:Default Game Mode:
When you load into this map, you will spawn with a Pillager Outpost directly in front of you. Do not approach this yet as you will be killed pretty quickly. Instead, what you are going to want to do is turn around and locate a couple of trees in order to gather some wood as you are going to need a weapon.*Alternatively, you can just make use of the materials within the bonus chest rather than have to spend time gathering them.
Gather enough wood to create planks in which you can use to create a crafting table. Once you have created the table, you are going to want to create a small bundle of wooden sticks, and then use the wood sticks and planks to create at least 1 wooden sword.
What you need to do next is approach the outpost and kill all of the Pillagers surrounding it. You may die once or twice doing this but you can just spawn again next to the outpost where you will be able to collect your sword again and continue slaying. Once all the Pillagers are dead, you can head on into the outpost where the Captain will be waiting upstairs on the top floor. You can identify the Captain as he carries a banner on his back. Kill him the same way as you did his army and the achievement should pop shortly after.
This achievement can also be combined with the following achievement:
After killing the Pillager Captain and gaining the buff, head on over to coordinates (1050, 68, -165)
and wait for a purple/magenta coloured bar to appear and fill up at the top center of your screen. Your achievement should pop shortly afterward.