Stick Fight: The Game

Options
Map: Any
Weapons: Pistols: Pistol
HP: 50

This won't work if you block a punch. It has to be bullet.

Grab a pistol with your 2nd controller. Get the 2 players close to each other and aim with your 2nd controller at your main account.
Hold both controllers in your hand, press to block using your main controller then immediately to shoot using the 2nd controller.
Now, throw the 2nd controller away, grab the main controller and quickly kill the dummy account.

I was able to pop it without a gun. I blocked a melee attack from a local co op partner and then finished them off and unlocked the achievement.

Game settings:
Map Any
Weapons None
Hp 1

I think it should be mentioned that the block occurs when you time it correctly while the stamina bar is still flashing. If blocked correctly it should create a sort of explosion that knocks the player back.

If blocked correctly you will not take damage and you can immediately (I took about 2 seconds) punch out the enemy in one hit since it is 0 HP.