if you've ever been launched into the void off the top of a pillar by the ender dragon before, you know that the dragon tends to fling things around like crazy. this is because it's center hitbox wants to push objects away really fast, proportional to how close it is to the center.
if you fire an arrow at the exact perfect spot (I'm talking insanely perfect - pixel and frame dependent, as well as needing the correct rng for the dragon's flight path) then you can exploit this to have the arrow be launched at incredible speeds directly into the dragon's hurtbox.
arrows in minecraft calculate their damage based on velocity. that's why barely charging a bow does very weak damage, while fully charging a bow does much more. however, there isn't a cap on this damage. you can theoretically one shot anything in the game no matter how strong, as long as you can get the arrow to travel fast enough. and that's exactly what happens here.
the final minute barrier being broken for ssg just shows how much dedication and commitment and knowledge and willpower the entire minecraft speedrunning community has.