Credit to Jack Trauma xx for finding this grinding spot in his Double Trouble guide. There are a lot of questions on some of the grinding in the game, and I hope to clear some of that up.
EXTRA NOTE: The Overkill Contracts people talk about playing are part of the Overkill Edition DLC with new copies of the game. People renting the game or buying used will not have these missions to play.
You can get all 3 overkill achievements in one session with this solution.
1) You will want to play a solo game on easy. (co-op doubles the grind but is an option if you want)
2) Load Chapter 23. Into the Light. (We will be grinding in Chapter 24 but you need to fill your Overkill meter)
3) Play through Chapter 23 and into 24 until you breach the room with the mounted machine gun in the back of the church.
3a) Make sure the AI does not use Overkill. I did not have a problem with this but I do hear he can activate it on his own. If he does use it, reload checkpoint.
4) When you breach the door with the mounted machine gun, you will get a checkpoint. This is where the grind starts.
5) Press UP on the D-pad while aiming at the mounted machine gun to have the AI jump on it. This will spawn the grenadier at the back of the room.
6) Take cover to the right of the AI against the wall. and wait for 2 grenades to hit the wall knocking a hole for you to shoot through.
7) Now to hit Overkill! To activate the AI's Overkill, press Down on the D-pad.
7a) For Moocher, only activate the AI's Overkill with Down on the D-pad.
7b) For Overkiller, only activate your Overkill with LB.
7c) For Double Trouble, activate both Overkill meters pressing Down on the D-pad and LB together. (there is room for delay if you need it)
8) while behind cover, look to the left of the room. There is a hallway upstairs that enemies spawn from. Using Overkill, kill the enemies as they run out of the hallway. Do not focus on the enemies in the back of the room because they are harder to hit. As you kill enemies running out of the hall, more will spawn and they are much easier to kill than the ones in the back of the room and makes best use of your Overkill.
9) Once Overkill is gone, pause the game and reload checkpoint. Repeat steps 5-9 until all 3 achievements are unlocked.
Side not: Stats will not update in the menu if you reload checkpoints but the kills still count. The game also counts all overkills from your overkill and your partners overkill so the number may not match up.