I waited until I had gotten all characters to A20 before attempting this. After having learned all of characters pretty in depth it became painfully obvious to me that Watcher is significantly stronger than the other 3 characters (although prior to watcher's existence I'd agree that Ironclad was the best for this achievement).
To put this into perspective a little bit, here's how many runs it took me to get each character to A20:
Ironclad: 54 runs
Silent: 66 runs
Defect: 87 runs
Watcher: 27 runs!
So with knowing this I figured Watcher was definitely the best character to get this achievement, so I went for it and got it on the first try (albeit with some luck).
Some things to take note of when going for this achievement:
Watcher is a great candidate for Boss Relic swap from Neow. You're hoping to get any energy relic, as you're trading an extra energy on 1 turn per combat for an extra energy for every turn per combat. On my run I got velvet choker which isn't necessarily the best for watcher, but I made it work.
You will want to try to path out as many campfires as possible so you can upgrade cards early as Watcher destroys act 1 with 4 energy. I did not have to heal once in act 1. One thing to note is I got offered an early Lesson Learned, which is great to get early as it is easy to draw out some fights and get even more upgrades. I'd recommend upgrading Eruption so it becomes 1 cost making it easier to get in big damage turns or to get extra energy from using it while in calm.
My general thought process when playing watcher is to get a lot of cards that help do a lot of damage in a few turns but also have quite a few cards that let you exit wrath when you need to.Some Watcher cards that will get you out of wrath are:
Vigilance (starter card)
Fear No Evil
Meditate (premium option, especially upgraded)
TranquilitySome Watcher cards to look out for that when I see I almost always take without question:
Talk to the Hand
Cut Through Fate
Blasphemy Some Watcher cards that I'll take often depending on how the current deck is looking and what I'm missing to make the deck stronger:
Sands of Time
Wave of the Hand
I realize I've listed a lot of cards here but the intent is to help people who are not as versed in Watcher identify cards that can help take their decks to the next level.
Even with the luck that I had on my attempt at this achievement I still made plenty of mistakes that almost cost me the run which will show you that there is quite some wiggle room to getting a winning run. For instance taking Alpha almost cost me my run as it clogged my starting hand and I rarely got to play Omega so it just gave me dead draws. Master Reality and Battle Hymn are usually a good combo but my deck was too big to utilize them more often than not so again, wasted draws. Another big problem I had was accidentally winning a second Eruption from the matching card event as it never got upgraded and I already had several cards to get into wrath. My deck overall would have been much stronger if I had kept it closer to 30 cards instead and also would have benefited from more strike removes.
All in all this achievement is very doable with Watcher with Boss Relic swap, just expect it to likely take several attempts for the stars to align. Last thing to note is to not accidentally take relics from chests/events/elites as its very easy to autopilot and take them by accident.
I'll post a screenshot below of my run and if anyone has any questions about the run or even for just general watcher advice, feel free to leave a comment.