To unlock all six ally achievements with only three playthroughs, when you start the game, focus on getting all six of your teammates. select two of them to play through the game with and keep those two until you complete the majority of the game. You will get the ally achievement for the teammate you recruited first. After getting it, replace that teammate with another one as soon as possible. After the next assignment you complete, you will then unlock the ally achievement for the second teammate.