For the majority achievement, you have to make sure you do things at certain times and obtain quests after/before certain planets. Some of the Citadel quests come after the third story planet, and some quests you have to complete before unlocking new clusters and systems. A lot of the UNC quests require flying to certain systems and hacking certain terminals.
As far as I know, you have to pretty much complete this entire list of sidequests (I'm sure there's one or two missing as it is) otherwise you will not get it. I was missing only a couple my first time through and I did not get it.
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