I think it should be possible to get all the armors in one play through. You would probably need to focus all your credits on armors though, and forgo upgrading weapons and purchasing weapon mods.
The 5 unique armors cost 250000 together. That's the same as a single Black Widow, and I was able to purchase one of those and upgrade nearly every weapon to level 5 in one play through.
The unique armors are available in the Citadel shops. But I wouldn't buy them for any other reason than to get the achievement. You can usually build a better setup using the individual components. Shepard is also 89% cooler without a helmet.
The individual armor components can be found in missions, or in the Citadel shops if you miss them. They tend to cost in the 2000-5000 credit range. There are 35 different components you can collect, so look to spend another 200K.
There are two additional unique armors that you can acquire. The Reckoner Armor requires you to have played the demo of Kingdoms of Amalur. The N7 Defender armor came with certain pre-orders.