Working with KrakenScorch here is a combined guide:
Your best bet to collect this achievement is through mutators. The following will help a lot:
1. "Two for One" (every time you draft a card you gain 2 copies of it.)
2. "Come Prepared" (adds 12 random cards to your starting deck.)
3. "Burn Bright" (+2 Energy per turn). This extra energy will help you deal with higher cost random cards that would likely otherwise be a dead card in early game.
Since this run includes random cards, it may be helpful to have cards that have "Consume". If a card does not have have it, it can be added at the Merchant of Magic with a Surgestone (20 gold).
Another helpful aspect to be on the lookout for are Draw cards, as this will help you navigate your deck during the run.
Another thing to keep in mind during the run is to consider taking the +Draw artifact from the mini-boss stages. Another viable option would be the +Space artifact if your run has a lot of unit cards.
Overall the goal should be to grab cards that compliment your deck and duplicate cards where you can and it makes sense.
KrakenScorch's original guide strongly recommended using a run with the Hellhorn as primary and the Awoken as secondary.
One proposed challenge run is the following:
The basic premise of the build is Hornbreaker with the following:
Armor 10 and Multistrike 1
Slay: Gain 10 Armor
Revenge: Gain Rage 3
Put it in either in the front or behind an imp or two and build its rage while adding armor to it.
I picked up Animus of Will and Shattered Shell for some added power behind Hornbreaker / on the other floors.
Artifacts (in order of collecting)
Blood for Blood
Light of Seraph
Ashes of the Fallen (Rage Imps with this kicks Hornbreaker into high gear)
Scorching Restraints (MORE RAGE)
Light of Seraph
Animus of Will - Heartstone and Strengthstone
Animus of Will - Heartstone
Shattered Shell - Frenzystone and Strengthstone
Train Steward x4
Dark Deal - Stackstone and Ember (would have had two but screwed up the second one by adding a Surgestone, do NOT do this as it adds 20 to the damage part of the card...which would damage your unit)
Steel Enhancer x2
Vine Grasp - Surgestone
Imp-Pressive - Surgestone and Eternalstone
Imp-Pressive - Surgestone
Pyre Shards x4
Sharpen - Emberstone
Reinforce - Emberstone