Army of Two

You can do this in China on single player fairly easy. Equip yourself with the M134. When the level starts hold your AI partner at the bottom of the steps. Run up the steps, get behind the first tree and fire on the 2 guards. when you kill one wait and then go into Overkill. After blowing up the bridge you can do the same going backwards. Rinse and repeat. If you need "Running Man" you can exchange weapons at the beginning with the AI and follow same directions as above. Make sure you go all the way back down to the hovercraft to the save point where it shows your money.

This will also get you pretty close to the $1,000,000 achievement.

If you've finished the game and still don't have this by normal play, the DLC veteran map Kiev is great for this too. The China method works well for money, but this way takes less time in the end- much shorter time between reload and frag.
Load Kiev mission -after the intro cut-scene you start in the subway rail area. Equip a high aggro weapon of course then proceed - there will be two guards on the platform - waste them then start shooting into the first open area of the platform - I got overkill prompt rather quickly even while on professional - make sure to put partner on non-aggro hold or he'll start killing everyone - then just take out anyone left until the timer runs out - reload checkpoint and go again - the reload of checkpoint is w/out the long cut-scene this time, however there is a short one as they enter the subway T.W.O. style.
Depending on how many enemies it took to hit overkill mode, you should have at least 4 or 5 kills left per reload.

- Happy Fraggin

You can get this achievement in both the single player mode (with a co-op partner or computer) or in multi player mode.

I would imagine it is best to do this in the multi player mode however I got this in a single player co-op match.

You will unlock this three different ways. If you play through the game twice/three time (to beat professional and easy mode, and maybe to get the My Virtual Friend achievement), if you boost the 1 billion dollar achievement (one guy with us got both the overkill achievements at around the 700 million mark), or boosting for it.

To get power mode overkill you will want all the aggro. If your playing with a AI partner put him on passive mode and max out your aggro meter (you will need to kill at least one person to max it out). Once it is maxed out you will need to fill up your dark red meter by continual gun fire when the dark red meter inside your red meter is full for 2 seconds or so, hit the A button when the overkill message comes up to go into Overkill mode. You will then need to kill 100 enemies to unlock this achievement.

If your planning on boosting for it either do it in multi player mode or in story mode right after a checkout with 7+ enemies in the room. You can continue to reload the last checkpoint to get this achievement (this is how I got it).