I too, just last night, finally beat my first normal run, with the Ironclad. I’ve managed to beat several daily climbs now, but this is my first “regular” win.
I credit my success to an upgraded Demon Form (gain 3 strength every turn) combined with liberal use of the card that doubles your strength. I also made good use of the 0 cost card that does damage and adds a copy to your deck along with a card that gives you two extra copies of an attack or power card in your hand - along with buffed strength, I was often able to do massive damage in one turn. I kept a fairly small deck, and got lucky with quite a lot of good relics.
The final boss was the Awakened (I’m not sure if it’s random or not - is it?), and he did actually kill me, but I had picked up the relic that lets you survive one time and get back 50% health. I normally wouldn’t pick that relic, but it was a boss relic, and the other two choices were worse.
It felt good to finally win a run through my own decent choices (and some amount of luck, of course).