Pretty self explanatory. I can confirm that you do NOT have to do it within the time limit, so take as much time as you need! However, traps will eventually re-arm themselves after being disarmed, so be extra careful. Thanks to Capn Beav for mentioning this.
If you kill any NPC, DON'T use the Blade of Woe! Any kill with it will make you Detected and void the achievement. Thanks to Pink Freud PhD for confirming this.
If anyone detects you for any reason and you lose time you can simply abandon the quest, which will bring you back to the Thieves Den where you can try the same heist again. Thanks to Dale Baldwin for confirming this.
The achievement should pop as soon as you approach Fa'ren-dar after you've collected the valuables.
I personally did this on the Glistening Cave one where you steal 7 jewels because it's a small area and easy to see everyone near you. Just make sure you know the guard's pattern and you'll be golden.
If anyone has any tips or criticisms to add to this solution, feel free to reply.