This achievement requires getting through five crypts and opening the treasure at the end without triggering any traps. Make sure you enable the challenge in the expedition menu before starting.
When you're in a crypt, always look down at the floor and avoid sprinting in areas you haven't been. Be especially careful when climbing up a ledge, as some traps are placed against the edge.
There are essentially two things to look out for: leg traps and collapsible floors.
Leg traps are simple to avoid by shooting them from a distance with an arrow, which will disable them.
The floors are a bit trickier and require careful jumping, usually from a sprint. If they collapse at all, even if you don't fall, the challenge will fail. And it can be extremely risky jumping them. Therefore, the safest way to do the challenge is to turn around and leave if you see one of these. Some layouts don't include this particular trap, and bailing instead of trying to jump them remove the biggest risk.
Note that, if you're having trouble finding five unique crypts with no floor traps, codices and sarcophagi can respawn if you run far enough away.