This achievement requires you to beat act 3 with the Watcher whilst carrying all three colored keys (one from an elite, one from a chest, and one from a rest area), and then beating the final boss in "The End" (Act 4). Note: If you do not have the other achievement in this DLC for "beating the game with the Watcher", you won't be able to unlock it if you have the keys. Effectively, going for this achievement in a run negates the other achievement during the run, so I would suggest attempting to beat a normal run and then go for completing the ending.
As with the other characters, there is no defined way to build your deck to achieve success - it largely depends on random events and your ability to assess your current situation and what additions to your deck will improve your odds of success. There is some skill needed for this, but also a lot of luck helps with the random card offerings/potions/relics you can receive.
Personally, I used the following page to work out some generic strategies with which to approach each attempt:
https://slay-the-spire.fandom.com/wiki/Watcher#StrategiesThe deck I used to beat the Ending the first time revolved around changing stances frequently to generate energy and recall Flurry of Blows to my hand (I had 4 by the end). I also got lucky with some really good relics and I kept my deck fairly trim. I tried a few other strategies that performed decent in Act 1, but really floundered in Act 2. The Stance Dancer type deck was the only one for me that scaled well enough to last the whole way through.