Under Night In-Birth (2012)

Every month, a phenomenon called the Hollow Night brings forth invisible, immortal creatures called Voids. They feed upon a power known as EXS, which they gain by attacking humans caught within the Hollow Night. Though the attack results in death or Void transformation of victims, anyone who survives becomes an In-Birth, gaining the ability to control EXS. After surviving a Void attack, high school student Hyde Kido receives the power to summon Insulator, a magical sword killing In-Births. A immortal girl named Linne offers to train him with powers on the condition that when he is ready, he will end her life. Caught in a battle by others vying for control over EXS, Hyde finds a way to survive until the next night.