All You Need Is Kill, Vol. 1 by Ryosuke Takeuchi

When the alien Mimics invade, Keiji Kiriya is just one of many recruits shoved into a suit of battle armor called a Jacket and sent out to kill. Keiji dies on the battlefield, only to be reborn each morning to fight and die again and again. On his 158th iteration, he gets a message from a mysterious ally–the female soldier known as the Full Metal Bitch. Is she the key to Keiji’s escape or his final death?