The dragon has 200hp, and arrows deal 2x their speed(in m/t) in damage. So in theory you only need 100m/t. But because air resistance and since the dragon quarters all damage that doesn't hit the head, you need more like 400-450m/t. And to get this in one tick from dragon knockback you need to be within ~.02m laterally of the tickle spot. You can stay there longer, but the dragon flies away too fast for it to matter.

Once you get the knockback you can just shoot the arrow, but getting it to hit the dragon is a challenge in of itself. In order to get into the spot you basically need to be inside the dragon's body hitbox. But entity hitboxes are only tangible from the outside, so your arrow straight up can't hit the dragon's main hitbox. Luckily the dragon has multiple hitboxes tho, so we can aim for these. Except we can't really aim for anything because the dragon's knockback completely overpowers the the arrow's initial velocity by like 100x. Instead we have to just rely on the knockback being in the right direction, which is based on your angle towards the tickle spot. So we're aiming for a .02m circle around the spot, but also only for certain slices of it that knock us towards the wings/head/tail hitboxes.(Except you can't hit the actual head hitbox afaik since it sits inside the neck hitbox, so you just hit that.)

That's also glossing over a pretty important part though, which is figuring out how to throw a pearl that tps you into those slices(this is the part that actually takes effort). The notable thing about this video is that none of the starting positions/dragon positions were selected special for this. Instead I wrote a program that takes a starting pos/dragon pos, and half solves/half bruteforces a series of angles that let you land a pearl into the right position. Which is epic sauce because it means I could (relatively) easily incorporate it into a real end fight.

It's easier said than done though, because we're not just trying to hit a .02m moving target- that's pretty easy because projectile collision is (mostly) continuous. We literally need the pearl's /actual/ position to land inside that small range, and then have it collide with the dragon a tick later. But pearls move like 1.5m at a time, so even if we pass through the .02 target, there's less than a 2% chance its position actually fell in the right spot. And we can't just fix it just by choosing a different pitch/yaw because the target is so small- you literally need to get a different starting position/velocity. Obviously I can't change position, but there is an easy way to change velocity since you also transfer your server velocity to pearls. See, when you sprint jump you get .2m/t of velocity in the direction of your current yaw. But your server yaw is delayed 1 tick from your client yaw, which can desync this added velocity. So skipping the logistics, you can sprint jump/throw a pearl in one direction, but with the added velocity of a sprint jump in another. The velocity change is almost nothing, but gets magnified over the trajectory so you basically always get a solution, even when you're only searching every .01 or even .1 degrees for each yaw/yaw/pitch. (I think I even saw some that gave like 10k+(actually i fixed a bug and got a 250k+ one), but that would just freeze the game :sob)