Described as a grueling "5.5 hour fight," they do wield a shield to parry (and use abilities), but damage is being done by way of raw punches. The fortitude required to pull off a run like this is frankly insane, as they rarely lose their cool during the run. If you want to check out the whole process, GinoMachino has a Twitch channel, and has titled the run "100 Punch Man."
The Godskin Duo are a tricky boss encounter, especially going in completely blind. While there are zones you can use in the arena to your advantage, and plenty of tricks/builds you can adapt to, the sheer chaos of the fight is tough to navigate your first time through. The gist is that both enemies are coming at you
Initially, I assumed that if you defeated both of them at the same time, the encounter would end. In my first blind pre-release review playthrough, I attempted to methodically bring both of them down to roughly 10% health, then defeat both of them simultaneously. Imagine my surprise when they both revived! Oops! Once I refocused and started to figure out when to take them down (and when their second phase was advantageous to trigger), everything clicked. But to be clear, I used weapons, not fists!
Elden Ring player beats Godskin Duo with their fists: