when you play Elder dragon, do you choose all targets right away? or do you choose 1 by 1 so you can kill them in a specific order.

No — you choose all of them at the same time.

Elder Dragon's "When you play me" ability is a single triggered ability with one target per location, so all of those targets are declared together when the ability is finalized and placed on the chain (Rule 355.5.b / 355.8). You don't get to pick one unit, let the damage resolve, then pick the next — your opponent can't be forced to react between individual targets, and you can't chain kills in sequence (contrast Falling Star, where both targets are also locked in at once).

Everything chosen is then dealt its 1 damage as one resolution, and any units that die to it all die in the same cleanup — so there's no ordering trick that lets you kill one, see what happens, then re-target. If you want targets locked after seeing a reaction, note the ordering instead runs the other way: targets go on the chain first, then your opponent gets priority and can react (Flash, Counter Strike, etc.), including moving units out of the location they were targeted at so they're no longer hit.