Like the mythical hydra, the Illuminati have many heads and even more hands. The minions of the Illuminati might work to their hidden master's ends without ever knowing the design of their work, or for whom they indeed work for.
Rather than making a baddy impossible to hit, consider giving it mega-hit points.
Super hard to hit leads to great player frustration. Allowing them to do damage leads to a sense of accomplishment. another variation of this would be to give the bad guy a forcefield that shows damage.You could also give them a mastermind ability that sluffs the damage of to minions who should be easy to kill.Once in a while a super high to hit encounter is ok ,but it should be few and far between.
Your mileage may vary