Again with the lack of sound. Well, one could construe it as a moment of silence for the run, as I just couldn't manage the second form without items.
As far as this fight goes, it is very dependent on seal procs. Freezing the archaisms helps too, but it's not strictly necessary. The main danger from them is their field wide charged attack, which has an incredibly fast cast time. Generally you'll want to stop this by freezing them (if you have time to...) or an S-Craft backed by an Impede 3 quartz.
Sealing Joachim is extremely helpful, but make sure to keep his speed debuffed regardless. His stealth craft gives him a massive speed boost, but if he's debuffed beforehand it will just negate said debuff. Letting him get the boost will result in him getting many turns in a row, and possibly S-Crafting you before you get a chance to respond.
Spreading out to the four corners of the field keeps him from hitting multiple characters with any of his crafts, including the S-Craft.