If you wanna do this solo, you should acquire the following skills: Sprinter, Fast Hands, Shinobi, Endurance, Dominator.
This achievement can be done solo or in co-op. When playing solo the vault may not spawn in the bedroom downstairs. If it does, restart the mission.

First off, take out all the guards and cameras. Use the dominator skill against the guards to make them handcuff themselves. Then pick up the the 5 missions items (random locations) and bring them to the roof. Find the vault and use the PC to disable the laser system. While the lasers are disabled you can take a bag of gold and bring it back to the roof. Do this until you have all the gold and throw it under the zipline. The achievement will pop after the mission is over.

Just a quick note: If the stars align, you can get this achievement solo. However, in order to do so, the vault will have to spawn on the second floor - the same floor as the desktop computer. Unfortunately, there's no way to tell where the vault is without actually playing the level, so prepare to reset often.

Even with the vault in the proper place, you'll need some perks to get through. These fall into two basic categories: subduing the five guards in the area and being able to dash to the vault quickly.

Subduing Guards:
Dominator (Aced) - Mastermind Tier 3
Smooth Talker (Basic) - Mastermind Tier 3
(Optional: Pumping Iron (Basic) - Enforcer Tier 2)
(Optional: Martial Arts (Basic) - Ghost Tier 3)
(Optional: Shinobi (Ace) - Ghost Tier 3)

Dominator is essential as you want as many guards as possible to surrender and cuff themselves. Oddly, guards seem to have no problem with one of their comrades kneeling down handcuffed, but will instantly sound the alarm when seeing a corpse. The same goes for cameras, so try not to kill a guard where he can be seen by a camera.

Unfortunately, guards will sometimes resist domination and you'll have no choice but to kill them. Smooth Talker helps because you can successfully answer at least four pagers before risking an alarm (as opposed to the standard two.) Domination is still preferable, as you're a sitting duck while answering a pager.

The optional skills will all boost your melee ability. If you don't have any suppressed guns, melee is the only stealthy option you have left if domination fails. Be careful when meleeing alerted (and un-dominatable) guards, as if you're not quick on the draw, they'll cuff you and sound the alarm, ending the mission.

Getting to the vault (and getting the gold out):
Endurance (Aced) - Mastermind Tier 1
Transporter (Basic) - Enforcer Tier 1
Sprinter (Aced) - Ghost Tier 1
Fast Hands (Aced) - Ghost Tier 2

After subduing the guards and smashing the cameras, all that's left is getting the gold out of the vault without sounding the alarm. Once you enter the override on the desktop computer, the motion sensors will turn off for about ten seconds. During this time, you'll have to sprint to the vault, bag one set of gold bars, and exit the vault before the motion sensors turn back on. (This is why it's only possible when the vault is on the same floor, and therefore closer to, the computer.)

I'm unsure if you only need to get one bag of gold or all eight to get this achievement, but getting all eight is ideal for getting a hefty payday out of the mission.