There are several "Team Attack" moves that can be performed with your brothers.
*If someone can confirm that they all count towards the 50 or if it is just the actual "Team Attack" move that is listed.*
When leveling your turtles each has several spec trees. Under the TEAM tree for all turtles, on the left side, is a spot to place a point for the "Team Attack." You only need to unlock that ability with one turtle as that brother can now initiate a "Team Attack" with the any of the others, however, none of the other brothers can initiate that attack unless you spend a point in the same place.
After Chapter 1, return to the Turtle HQ and go into the Dojo. Here there are several scenarios you can choose from to train. The fastest way I found to do this was to choose Team Training. The official "Team Attack" move is Hold RT + A, however you must have at least a single special bar filled.
Simply beat the hell out the training robots and every time you fill the special bar move towards one of your brothers and Hold RT + A. Note that you must be facing enemies for the attack to activate. If there are no training bots near you the turtle you are controlling will just jump.