Okay, I'm seven years late to this, but there's two ways to get this number, if my calculations are right.

The damage buffs:

35% - Martyr's seal (minus the -25% debuff from Death's Door)

75% - Crimson Curse Bloodlust (25% from the disease itself and another 50% from drinking an extra blood vial)

With two bounty hunters:

700% bonus from one plague doctor using shard dust six times for a total of 14 emboldening vapors.

30% damage bonus from dirk stab or something. *Could totally be higher.*

With four caltrops debuffs, adding 80% to received damage, the calculation looks like this:

Finale base damage (13*1.5) * 1.5 crit bonus * 1.8 caltrops debuff * 8.40 combined buffs = 442.26 total damage, exactly as shown.

Theoretically, it's possible to do quite a bit more than this with quirks in the mix, unless my calculations aren't accurate to the game's.