UrlJudge's statement on tag battles not counting is wrong. Tag battle outfits DO unlock as of the latest patch release/Komplete edition.
Now, if you have complete edition, this is very important, do NOT go to Nekropolis until you are sure you have unlocked every character's alternate outfit (Mileena's 3rd doesn't count).
Basically, there is a bug in Komplete edition where if you unlock all your outfits from the ladder, the achievement will not unlock. Here's the fix (or if you want to do this first to save you the hassel of tag battles).
On the start of a new game (back up your old save to a USB if you have already gotten this far and bugged a bit).
Play around until you get 10,000 gold. Then, go find the secret chests (Plenty of youtube videos online to show you where they are). Now, go buy all the costumes from the Krypt with the 30,000 gold you'll have by the time you pop the 4 chests.
Next step, go to Nekropolis and do not leave until you have examined EVERY character available (ignore DLC guys and Cyber Sub Zero), if you go from left to right, when Quan Chi's alt costume announcement appears your achievement should unlock.
At this time, you can resume play as normal (or if you had to back up your original save because of the achievement glitching, you can reload it back from the USB now and resume your playthrough).