The easiest way to unlock costumes is through tag team matches in Survival, Time Attack or Arcade mode. You can use the mode you like. If you complete a run, both members of your tag team will unlock their next unlockable costume.

At first I thought you could only unlock one costume per level per team, because it works that way when you fight single player, but tag team matches keep unlocking costumes every time you complete them, even if you play them with the same team, on the same difficulty.

This way, you can quickly and easily unlock all costumes, even if you play just on the easiest difficulty level.

This is also a great time to figure out the special tag team combinations. Most of these combinations have special throw moves, and each has special animations when a fight starts and when you win.

For a complete list, see this post here: http://www.gamefaqs.com/boards/835976-dead-or-alive-5-last-round/71281189.