What the achievement asks
Collect ten Lost Supplies during climbing world quests. Five points, account-wide.
One per world quest, and only in the right zones
Exactly one Lost Supplies spawns per climbing world quest. There is no second pile hidden further up, so once you have found it that quest is finished as far as this achievement goes.
Climbing world quests appear in the four original Dragonflight zones. Those in Zaralek Cavern do not count, which is a genuine trap: players have found and looted Lost Supplies during Spearheading Acquisition and seen no progress at all. The Forbidden Reach and the Emerald Dream are equally not the place for this.
Taken at face value that is ten separate climbing world quests, spread over however many rotations it takes for them to come round.
The way to compress it
Progress is now shared across your warband, and the pile is in the same place for every character. So you can log onto one character, take the climbing world quest, collect the Lost Supplies, log onto the next, and collect the same pile again at the same spot.
Six characters visiting one world quest is six of the ten in about as many minutes. That turns an achievement gated by world quest rotation into an afternoon, and it is by far the most useful thing to know about it.
If the loot window misbehaves
This achievement was broken for a long stretch of the expansion. The loot window would open, glitch, and award nothing, and players reported it happening on perfectly ordinary quests in the four main zones.
It was reported fixed in patch 11.0.5. If you do hit it, the pile is spent and there is no way to recover that quest, so simply move to the next one rather than trying to re-loot.
Where it fits
One of eight under Wake Me Up, which rewards a Bestowed Ohuna Spotter and is a piece of A World Awoken.