This is how I unlocked the achievement and I only played
as JILL VALENTINE
Normal difficulty playthrough ("Like climbing a mountain" from the main menu)2.
Normal+ playthrough (New Game Plus) ("Once Again..." from the main menu)3.
Real Survival Mode playthrough4.
Invisible Enemy Mode playthrough
Everything of course on the same save-file and that's also the order I played the game.Additional notes
-Both RESIDENT EVIL 5 - BSAA
outfits for each character are available from the beginning.
-Complete the game once with Jill on any difficulty to unlock Jill's ARMY
-Complete the game a second time (same save-file NG+) with her to unlock Jill's RESIDENT EVIL 3
Complete the game once with Chris on any difficulty to unlock Chris' THE MEXICAN
Complete the game a second time (same save-file NG+) with him to unlock Chris' ALTERNATE S.T.A.R.S.
As I stated on the top that's how I unlocked them, never played with Chris Redfield. So either play it four times with Jill Valentine or twice with her on twice with Chris. Just make sure IT'S ALWAYS ON THE SAME SAVE-FILE!!!
If you guys find a faster/different way to unlock this let me know. Hope this helps!