Max Payne 3

NOTE: It has come to my attention that a patch HAS moved this solution from Checkpoint 17 of Chapter V to Checkpoint 18 of Chapter V.

I found this easiest to get on Checkpoint 17 18 of Chapter V. When you spawn, wait a few seconds for your Adrenaline Meter to fill, then activate Bullet Time and go to town.
There are four enemies in the first boat, and then six or seven more will pull up behind it. Also, getting six kills, deactivating Bullet Time, activating again, and getting four more kills does not seem to work, I believe they all must come during the same activation.

The achievement will pop as long as you dispatch 10 enemies before running out of Adrenaline, aim does not matter. (I'm horrid at this game and I did it in Free Aim.)

Tips from Commenters!:

Also, any difficulty level or aiming mode works, so feel free to go on Easy with Hard Lock. (Thanks Wyndo and Markyshizzle!)

There may also be a problem if your gun overheats, so try not to let that happen. (Thanks Survivor Seven!)

Chapter: 5, Checkpoint: 14

Difficulty: Easy, Hard Lock

This checkpoint will start you with a few enemies on a landing to your left, then then guy who throws a grenade at you. Progress past this area and head a little further up river. There will be a few guys on your right before the landing, so kill them, but don't kill the three further down.

Once you get to the next area, there will be three guys on your right, don't kill them straight away. At this point you want to wait for another group of enemies to appear in the building just across from you. Once they're in hiding, your meter should be full. Click the RS or RB and start to kill the three guys on the landing to the right. This will cause more enemies to spawn.

Quickly direct your attention to the enemies hiding in the building and kill everyone in sight. By the time your meter runs out you should have 10 kills.

If the description is hard to follow, the video below will give you further direction.

10 Bullet Time® Kills In A Row

You will need to get 10 kills in one bullet time for this achievement will unlock, follow the video guide and you should have no issues getting this.

The other solutions sounded more complex then I felt it should be so I tried something else and it worked out first try with ease.

Chapter 10
Checkpoint 11
Easy with Hard Lock
Gas Station Group
Activate bullet time and get 10 kills

This is the bus ride. The second group of guys you come to by the gas station has enough guys and they are all bunched up together. Activate bullet time and fire away, if you run out and didn't kill everyone just reload the checkpoint and try again, since you're only about 10 seconds in it doesn't take long for more attempts but I got this first try.

Not sure if it makes a difference but I did not blow up the gas station when I got this. Not on purpose, just was aiming for the guys more.

Might be worth noting that my original intention was to activate bullet time late on the gas station group with the hopes that the next group that spawns in the distance would help round out the number but I ended up getting the achievement on the first group.