This can be done online or offline. In order to obtain this achievement, you must complete the levels from the first level (Home Castle) to the fourth level (Barbarian Boss) without attacking. You do this by either playing online with another person, or using another controller.
If you want to use another controller, simply kill all the enemies with the second controller, leaving the player you want to get the achievement alone.
If you want to get this online, simply get a friend to kill all the enemies while you sit back and dodge attacks.