For this, you need to have a DLC costume equipped on a character and use them to clear a stage.
To get the costumes themselves, however, will not be as direct as you think. If you have a preorder costume, those can be used immediately. Otherwise, you will instead need to purchase costumes from the Add-On section of the original Warriors Orochi 3 for the 360. The game will notice that your live account has purchased the costumes and unlock them for Ultimate as well.
To switch to the costumes, on the Team select screen, choose the character you want, then hit the the costume select button. The game will then cycle through the available costumes. You can tell if an outfit is DLC or not by the color of the little guy with a number by the characters name. Blue is base game, red is DLC. Alternatively, you can select the view model option and choose the costume that way if you want to see the outfit.
As a bonus, for completing this challenge, you will be awarded 250,000 growth points. This is of course, more than enough to break the early game as you can propel a character up 50+ levels with that reward.