Neverwinter

WARNING: You are unlikely to be able to unlock this achievement if you don't have a non-Strength attribute of at least 25*. You will need to re-roll your character or do it with another character in order to unlock this achievement.

*See Ways to Improve Your Chances below if you have 22-24 in one of the required attributes.

Solution
This can be found in The Maze Engine Campaign, Act 3, Mission 6: Strange Concoctions, which becomes available from Bruenor Battlehammer in Mantol-Derith about 15 days into the Campaign.

Bruenor will send you to see Lucas Shaneway III who will challenge you to a drinking contest. You will be asked to choose which attribute you want to use to try and beat Lucas with, with the exception of Strength.

Your success at each drink is based on classic D&D dice rolls, so there's no guaranteed way to win it. If you succeed at all three drinking challenges, you will unlock the achievement.

Ways to improve your chances

The following can be stacked in order to grant +3 temporary attribute points.

1. Make sure to stand in a campfire (there's one right behind Bruenor) for a few seconds. This will give you the Campfire buff for 15 minutes, which gives you a +1 to each attribute. This is denoted by a flame icon in the buff bar under your name. Note: the Mending Wounds buff is also denoted by a flame icon.

2. The Elixir of Fate can be purchased from the Vault of Piety or from the Auction House. This will increase all of your attributes by +1.

3. The Potion of Heroism can be purchased from Thradisar Starwise in Sharandar or from the Auction House. This will increase your primary and secondary attributes by +1.

When you fail, press instead of continuing with .. This will allow you to exit the conversation and immediately try again.

Thanks to Reaver Lion for this trick.

If you do accidentally continue after failing, see DeadlyPikachu 's solution for how to bypass the 15 minute cooldown on accepting the mission.

Down-voting
If you're going to down vote this solution, at least have the courage to comment and tell me why.

This isn't really a solution but i can confirm i just got this on my Devoted Cleric. All i did was click the wisdom option that says "lets not drink and pay attention to the task" or something. Since i have 29 wisdom the achievement popped. So basically just pick whichever you have the highest in and it should work i suppose. Should save you a lot of effort from all the other solutions saying go do this and that.

This is just going off the previous solutions, this is pretty much luck and if you're like me that's a lot of 15 minute cooldowns. So a way to break the 15 minute cool down and retry immediately is to delete the quest if you fail it and go and pick it up again. Hope this saves time for someone.

Boundless Ability
You succeeded in an ability checks when drinking with Lucas Shaneway III.

this achievement is easy to miss or fail if you have a lower item level character, how ever if you have a class with a non strength attribute of 25 or more it is very easy to unlock. This video will show you how