To unlock the Halo you must find the Bible spacebar item usually available in shops if you are lucky enough (one of the 15 cent items). The Bible has a brown cover with a black cross on it, be sure not to confuse it with the Book of Revelations which has the same icon with different colours.
Once you have the Bible keep it until you reach the fight against Mom in Depths/Necropolis II and use it once the fight begins as it instantly kills both Mom and Moms Heart. As soon as you use it to defeat Mom the Halo will unlock.