What the achievement asks
Find and open all the Sturdy Chests hidden in Archival Assault. Five points, account-wide.
How Sturdy Chests work
Every delve hides four or five Sturdy Chests. They are one-time treasures: once looted, that chest is done for your account for good, so there is nothing to farm and no respawn to wait on.
Most people collect the whole set in a single run, but not always. Some chests only appear during certain story variants. If you have swept the delve and one coordinate is stubbornly empty, that is the reason, and the answer is to come back on a day when a different story is running rather than to search harder.
The tier makes no difference here. Run the delve at whatever difficulty you find comfortable, ignore the objective, and walk the chest list.
Getting there
Archival Assault is in K'aresh. Delves are permanent, labelled icons on the zone map, so there is no coordinate to hunt for: open the map and click the delve.
The four chests, and the Phase Cutter
Archival Assault is the one delve where the chests are a movement puzzle rather than a list of coordinates. The tool for all four is the Phase Cutter ability the delve gives you, which lets you cross gaps and pass through barriers, and which cancels almost all falling damage. Walking over an Energy Condenser recharges it.
On the pipe above the Crystal Chamber. Drop from a higher level and use the Phase Cutter to steer onto the pipe. You have to aim: the pipe is narrow and there is nothing below it.
Behind the purple barrier. From the second ring up from the bottom, go to the south corner and drop to the platform with the closed door, using the Phase Cutter so you survive. Look left for the large hole in the wall with stairs behind it, cut across into it, then use the Phase Cutter again to pass straight through the barrier.
At the top of the stairwell. From the highest level of the arcane conservatory, take the waygates across to the cluttered room and walk through it to the staircase.
Above the Crystal Chamber, one level up. Around 46 25 there is a waygate. Phase Cutter across to the adjacent platform from above, then take that waygate up to the chest.
Wear a parasol or a parachute if you have one. It is not required, since the Phase Cutter covers the falls, but it makes the long descents controllable rather than a gamble.
The stories that may hide a chest
If a chest will not appear, the delve's story variants are Relic Retrieval, Shadowed Wings, Smash and Jab and Waygate Wiles. Come back on a day when a different one is running.
Where it fits
One of the pieces of Glory of the War Within Delver, which rewards the Ivory Goliathus mount and is part of Worldsoul-Searching, the War Within meta.