BioShock Infinite

Once you hit shanty town (Chapter: Shanty Town, for those that may have progressed further than this point and want to re-visit it via chapter select) go straight forward and into The Graveyard Shift which is a small bar - you'll see a nice autosave as you enter, here's where the fun begins.

Grab the absinthe from the small crate to the right of the entrance or grab the bottles on the main table and the whisky from the end of the bar - then whilst your screen is blurry charge up devils kiss and plop it down near one of the group sat round the main table in the middle of the room, it should get you the achievement quite easily.

Worked for me on hard difficulty and once it did I just reloaded checkpoint and everything was back as it was.

Video here:
(Thanks for granting me the permission to use it Maka91)

Edit: you can spread the kills out over a few checkpoint reloads if you don't get all 5 at once as they still apply when you reset the bar. (Thanks slam123 & fooga for letting me know about that)

Though there's already another great soluton for achievement, I still wanted to tell you the way I did it, which I found the easiest and earliest possible in the game. I did it on my 2nd playtrough on 1999 mode so really, you should have no trouble getting it this way.

Just after you get your magnetic shield, you enter the bar/church or whatever it is, the place with all the crows. The first room has a staircase in the middle, and on the left and right are 2 big rooms with on the left a bar and on the right tables with lots of fruit. It's impossible to miss.

As you enter this "bar", go to the left and you'll see a guy sitting on a chair and another guy walking towards him. Don't shoot them yet, Just walk/run past them to behind the bar and crouch (B), then drink yourself silly. Over the bar there should be 4 a 5 bottles of wine/whiskey/beer and when you get to the end of the bar, a guy's sitting there and he'll see you. Just spray him down with your machine gun and the other 3 will try to get you, easily kill them off too. You'll only get 4 out of 5 this way for the achievement but reload the last chapter and you'll begin right before this bar again :D Good luck, you should have no problem getting it this way!

This achievement is easily attainable on the chapter called The Sky Line. If you are selecting this mission from the load chapter menu it is called Monument Island Gateway. You come to a point in the campaign when you have to reach Monument Island to find Elizabeth (which is early on in the campaign). When you step aboard the flying freight to reach Monument Island the mechanized captain on the freight will tell you that the freight to Monument Island is closed and that you have to take the sky line. So grapple on to the sky line and at about one quarter of the way on the sky line ride (slowing yourself down by pressing down on the d pad to make this tower easier to find) there will be a tower called Monument Island Maintenance on the left side of the sky line. This will be the first maintenance tower you will see, not to be confused with the second maintenance tower. Jump off the sky line onto this tower and you will find two enemies. One enemy at the front of the tower, and the other is at the back of it along with 7-8 beers on some crates. Be sure not to sky line strike the first enemy as this will prolong the achievement. After killing these two maintenance dudes (while drunk) reload checkpoint and it will take you back to just before you grapple on the sky line. So rinse and repeat until you get your 5 kills while drunk. Quick and easy.