Dark Side Battles are unlocked once you have collected 3 dark side characters and you have reached player level 12.
You fight with the dark side characters that you have collected and unlocked along your journey through this game.
As with Light Side Battles, the game starts of quite easy and offers a good opportunity to collect resources for leveling up both your light and dark side characters.
So if you have got to a point in the light side battles that you just can't get past, focus on the dark side battles for a bit and try to level up your light side characters to so you get past the stage you are stuck at.