In order for the trophy to pop you actually need to kill an enemy whilst buddied up (not just buddy-up) so find yourself a level with some enemies to kill (I used Barrels Out Of Bond - The Elven Gate). Then one by one roll through each of the thirteen Dwarfs taking turns to kill an enemy.
There are 13 Dwarfs you need to buddy up:
Balin
Bifur
Bofur
Bombur
Dori
Dwalin
Fili
Kili
Gloin
Nori
Oin
Ori
Thorin
If looking at your characters selection left to right they start from the 11th character on the top line to the 4th character on the 2nd line.
You need to initate the buddy-up whilst using one of the Dwarfs listed above (I also set the non-active character as someone other than one of the Dwarfs i.e. Sam).