A buddy attack consists of having two compatible characters, such as two different dwarven characters, selecting one of them, then walking near another one and pressing "B". You should then see yourselves link up, either side by side, or one on top of the other.
When in this stance with two connected, "buddied up" characters, simply attack enemies as you normally would by pressing "X". I am not sure if simply hitting the enemy counts as an attack, so to be safe, just make sure to kill each enemy all the way.
Doing this 50 times over the course of your game will unlock the achievement. It is much easier to accomplish during missions, but there are a few side missions that send enemies at you.
If anyone can confirm whether or not you have to kill them for the "buddy attack" to count, please let me know so that I can update this and be the most helpful.
Feel free to add me as a friend if you enjoy my guides, and please PM me if you have any unique concerns or questions.
Happy Hunting!
-Dan