Won twice now with the Ironclad so here are my thoughts on what works and what doesn't work.
First off, Relics > Cards. Cards require you to draw and play them while relic effects are constant. This means that you generally want to go with the ? spaces over the smaller monsters. You still need cards but you'll have plenty of opportunities to add to your deck. It's certainly true that not every ? is going to get you a relic but they're the only way you're going to see them drop them outside of elite monsters/bosses. Elite Monsters always felt a bit more risky and draining that I wanted to endure so I tried to avoid them.
Secondly, you need extra energy from somewhere. Relics are your best source but cards that give you energy can also substitute for what your energy needs. You can't beat the later monsters if you're only playing 3 cards a turn, even the upgraded cards aren't strong enough to beat the enemy monsters. A mix of draw + extra energy is required if you're going to get through the 3rd map.
Of my two wins, the block focused one was the easier. The main card for this is barricade which lets your block persist between rounds and body slam which converts the block into 50-60 damage hits. Grab all the block cards you can and you can outpace all the incoming damage. It's actually a bit rough in the early turns as you're playing power cards that aren't directly effecting the battle but once you get rage and juggernaut stacks to go with your barricade, you're going to win that fight.
The second win was Rampage + Searing Blows + Headbutt. I kept my deck as small as possible and used 1-2 cards for a majority of my damage and focused on playing them as often as possible. When your rampage is hitting for 60+ things die pretty quickly.
I've tried doing a strength build but it wasn't that success even when starting with limit-break which lets you double your strength. The ramp up time is too long and I died in the 3rd map. I still need to try the other class and see how it feels.