There are a lot of ways to do this. I did it in an Ironclad run and here is my results screen:
To clarify, you cannot have any cards in your deck with a blue (uncommon) or yellow (rare) banner under the card name. These were common cards added to my deck:
Bash and Defend are Starter cards.
Body Slam was the key. Upgraded, it costs 0. Shrug it Off and Pommel Strike were useful for card draw. True Grit was useful to thin out cards throughout combat until I was able to remove them permanently and when upgraded, you choose the card to Exhaust. Warcry was a random late add that draws two cards when upgraded so it was a one time free card draw.
I had some good luck with my relics, as well, particularly one that adds, then removes 3 Strength on turn one and another that starts you with an artifact, effectively preventing the 3 Strength loss (making it permanent).