In order to obtain this achievement you'll basically have to beat every level in the game without dying. You can obtain this in new game + as well.
PLAINS is the first level you play and acts like the tutorial level. These checkpoints are protected and CANNOT be broken. So don't worry about those.
The final level has one checkpoint. It's unbreakable as well.
Essentially I got towards the end of the game, and then I replayed every Knights of No Order levels. Some of them got a bit frustrating. The propeller knight level is the worst :/ because if you die on the boss you basically wasted approximately 10 minutes each attempt. It's a long level so good luck and pat yourself on the back when that one is done.
Although the description for the achievement may seem daunting, it really isn't. Just take your time and you'll be able to complete all of these levels and destroy all the checkpoints.
The last two levels before the final level are definitely difficult as well, but after trial and error you'll be getting through them eventually.
You'll need to finish your playthrough completely for the achievement to pop if you in go in order. Otherwise the achievement will pop once you complete whichever level you missed a checkpoint on.