If you target the opponent’s monster with the effect of “B.E.S. Crystal Core”, and an effect is chained that causes it to no longer be on your opponent’s side of the field (such as “Remove Brainwashing” or “Enemy Controller”), the effect of “B.E.S. Crystal Core” is not applied.
The effect of “B.E.S. Crystal Core” that destroys itself during the damage step cannot be chained to.