According to Kotaku, you need to follow these steps to receive this glorious inebriated mission:
Own the Diamond Casino penthouse
Head to the public bar and keep taking shots of Macbeth Whisky
Get sloshed so that you get blacked out and wake up elsewhere
Where you wake up will be random, so you may need to keep trying until you wake up very far away from the casino. You’ll know you did it correctly when you wake up with paramedics tending you.The casino manager will ask how your hangover was, thus kicking off the mission. Good luck, and god speed.