The guide provided by the team at the Mass Effect Wiki site will help you to unlock this trophy. I used this guide on both the Xbox and the PlayStation.
All credit goes to the wiki, I am only sharing my resource with fellow players who might need some help.http://masseffect.wikia.com/wiki/Completionist_Achievement_G...
To unlock this trophy you need to have completed at least 45 assignments and pretty much all of the main story missions. Depending on which squad members you have on your party while completing your missions and assignments, depends on which 'Ally' trophies you will unlock.
If you want the 'Asari Ally' and the 'Turian Ally' trophies for example, follow their guide while only ever using Garrus and Liara on your team once you have recruited them. Liara will take longer than the other members as she requires 50 assignments.
Do not try to do this for Ashley and Kaidan together in one playthrough, you won't complete enough assignments for them both, so use them in separate playthroughs.
You will have to follow their guide for a total of three playthroughs to unlock all of the 'Ally' trophies.