An Army of Four? No problem

That's right, I can use big words too

I started Xcom Enemy Within again with the sole purpose of gaining this achievement, and I was terrified that I would be in deep shit by mid-late game when the big guns began coming out.
Turns out... No. Not at all. The hardest part of the game with only four soldiers is picking what classes you don't want in your standard setup.  And quite frankly, it's the heavy.

Every other class gives you everything you need, whereas the heavy... well he gives you rockets.  Which i don't use anyway.  I probably should, but I don't.

Everything else though?  Fantastic.  Support class for the obvious healing of 10-12 damage depending on who has what medal; Assault Class for the excessive amounts of damage you can pump away, at a guaranteed chance because of either proximity or aim bonuses from medals; Sniper because of "In the Zone" which will deal with those pesky low health enemies that don't take cover and die to a gust of wind; and the MEC Trooper because of the extreme damage output with the Kinetic Fist and it's heavy weapon, the speed at which it crosses the battlefield, and the awesome Robocop voice.

And that's how I ran through Xcom: Enemy Within on Classic without purchasing a Squad Size upgrade.

No, the game did not adjust to my squad size, I still fought about 40 enemies when the HQ was assaulted, including 3 sectopods. No, I did not get overrun every time I went and did an EXALT Mission, because they just aren't that dangerous. No, I did not have any Second Wave features active.  And Yes I was reckless with my troops, especially with my MEC who was always in the middle of the enemies because his damage resistance is the best when within 4 tiles of a target... That is, if they have survived that long.