Quests in the game are akin to favors. Fellow NPC Inmates with GREEN EXCLAMATION points / marks above their head have quests to give. The quest they have is random. If you are solely going for the achievement you can keep declining the quest they have and then cycle for a new quest until you get one that reads Eternally Grateful.
There will be three quests you'll need to complete for the achievement. You will need either 60 or 70 Intellect depending on the route you take to complete the achievement. Intellect can be increased by going to the library and completing a mini-game involving holding the
for periods of time. You can find the Library on the lower left on the map. First
, The NPC will task you with getting a book and returning it to them. This book will appear on your map by the sorry game piece symbol (pin) and will be in an "easy" desk (One that doesn't require keys or such to access). Grab the book out of the marked desk and head back to this same NPC. There can be multiple occurrences of this quest going on simultaneously (i.e. two inmates have this quest) so make sure to go back to the same guy you completed round 1 with. Second
, They will then task you with getting a Stone Tablet. Go to the marked on map desk and obtain it then deliver it to them. This item will be in a "hard" desk.
There are two ways to get to this desk:
1) The first way to get to the desk is to use a red key or red key copy and go through the doors to get to the desk. This will require 60 Intellect and finding which guard has the red key. Make yourself a copy of the red key and be sure to have a disguise since part of the path is outdoors. You can craft a medic outfit with your inmate clothes + bleach easy enough. Doing this way will require you to fight guards.
2) The second way to get to the desk is a path you can take via a grappling hook. This will allow you to circumvent the red key door. You will see tiny arrows marked on the ground near a grapple point. Once you're lined up with the grapple point with grapple hook in hand your cursor will turn green and show a repel symbol. This way will require you to have intellect 70. You will need to find / buy a grapple hook head and a piece of rope to craft the grapple hook. Also be sure to have a disguise. You can craft a medic outfit with your inmate clothes + bleach easy enough. Doing this way will not require you to fight any guards.
Either way you get to the desk. Grab the stone tablet and return it to the quest giver NPC and then start the third and final quest from that same NPC.Third
, They will task you with retrieving the "Vessel of Eternal Youthfullness, Wealth, Good Looks, Etc.". This will be on a fellow inmate so you will need to beat the marked inmate up and then loot it off their body. The item you are looking for on their person is a Holy Grail looking object called the "Cheap Plastic Cup". Return this to the quest giver and your achievement will unlock!