There are multiple ways to get this one done, but the way I did it was with the ironclad. You're hunting for the 3 next combats have 1 hp blessing, which you're actually much more likely to get after a totally failed run (where you don't even reach first boss), and then trying to get the card 'whirlwind' from the first 3 fights, or any shop you find.
You want to prioritise upgrading whirlwind, and then anything that can give you strength. Strength will affect whirlwind multiple times as it's a multi hit move. Take any energy relics you get offered to make whirlwind more effective, take good strength scaling (flex in a small deck where you're more likely to have a limit break in the same turn, spot weakness in a bigger one) and spin to win.
There is more wiggle room on this than you might think. I finished pretty comfortably with 3 minutes to spare.
I imagine this is doable on the silent in a run where you get offered dramatic entrances and backstabs for immediate burst damage, but I've only done it with whirlwind myself.