[{bar:[{foo:[{v_code:"first_vcode",_id:"first_id"}]},{foo:[{v_code:"second_vcode",_id:"second_id"}]}]},{bar:[{foo:[{v_code:"second_first_vcode",_id:"second_first_id"}]},{foo:[{v_code:"second_second_vcode",_id:"second_second_id"}]}]}]

db.collection.update({"bar.foo.v_code":"first_vcode"},{$pull:{bar:{foo:{$elemMatch:{v_code:"first_vcode"}}}}})