It says her ability "If a monster that battles with this monster is a Fiend or Zombie- Type monster, destroy that monster at the end of the Damage Step."

So would Spirit Reaper be destroyed by her after the battle. Thanks.

This should realy go in rulings just to let you know.

And yes, reaper will go, it's only protected from being destroyed directly in battle, battle related effects still go though.

Yes...Spirit Reaper will still be destroyed since it is NOT the battle itself destroying it (damage calculations and all), but the card effect.

Think of it as similar to attacking a face-down, Defense Position monster with Mystic Swordsman LV2, Sasuke Samurai, Paladin of White Dragon, etc.