Mass-effect – What’s the minimum required number of playthroughs needed to get all trophies/achievements

The quickest way to complete all the achievements (assuming you have sufficient skill level) would be to do it like this:

• Complete the campaign on Brutal, this will give you all the mission achievements below that require you to do it on hard difficulty as well (though in all honesty I had to do it twice, once on hard (also my first play through) to get through everything and then again on Brutal just to get it done). Also I did one on normal and only did the required missions to get through the game for the "Hurry up it's Raid Night" Achievement.
• To get all the Armory related achievements, on your normal/rush play through, save up all your money, buy all of one tier up upgrades (which will then give you the achievement) then reload your game and buy another tier. Make sure you don't save as it will give you all your money back at the reload point.
• With the ladder achievements, play random. When you get a win with random, it will also count as the race you randomed as. So random race as Protoss when you start the game you will get credit for one win as random and one win as Protoss. This goes the same with the Co-op games vs. AI.
• All the other random ones like, "Kill a full medivac", "Regen 500 HP on a roach", get "50 kills with one unit" (I BC rushed for this one and sent SCVs to repair), will all come in time as you get each race.
• Same rules apply with the co-op ones because most of them are race related (beat it on Random, gives you credit for random and the race you played as). Also for the difficulty related ones, do them on insane and they will give you credit for all the lower difficulties. Beat it on Insane and get credit for Very Hard, Hard, and Medium.

I believe most, if not all, of the accumulative achievements are tracked across multiple playthroughs. Like the moose finding achievement, I know I have been using several playthroughs trying to get that and so far it has tracked my progress accross all of them.