You can use your DLC skins for your first playthrough, rather than waiting to complete the storyline.

1. Load up the game, and load your save game.

2. In the menu before hitting "Continue Story", enter the following code with your keyboard or gamepad:
LEFT, LEFT, DOWN, DOWN, LEFT, LEFT, RIGHT, UP UP, DOWN
The game will make a sound when entered correctly.

3. Select "Continue Story". You will be given the option of using any of the Batman DLC skins.

Tadaa. Simple.

It appears that you will have to enter this code every time you wish to use a DLC skin.

EDIT: This will NOT disable achievements.