To unlock this achievement, you need to complete Act I of the Doomsday Heist as any role.
To do that, you'll need to complete 3 set-up missions and then the finale.
Each set-up mission consists of a prep phase, with infinite lives, and an actual set-up with the usual team lives (1 additional team life if you're playing on normal, none if you're playing on hard).
So basically, the host (heist leader) needs to have unlocked the Getting Started achievement (which is for meeting the requirements to be able to host heists) and has to pay for the set-up cost (6,500 if I remember correctly).
The host/leader may need to register as CEO, VIP or MC President (even if they've done it before). To do that, hold the back button
and use down
on your d-pad to get to the Securo Serv menu, enter it and select the option to register as whatever you are. (I completed the heist on 2 different days and on the 2nd day I had to register again, so I think you may need to do it each time).
After that, the leader will be able to access the hesit screen and start each of the set-up missions. Once each of the 3 prep phases and proper set-up phases are completed, you (the leader) will get a message from Lester on your phone saying that you can now complete the heist finale. The total reward is 650,000 to be split among all players (that's on normal, I haven't played on hard yet, I don't know if the reward is higher then).
You unlock this achievement when you successfully complete the finale.