Although Mystique has shapeshifting powers, that's not the only thing that makes her dangerous. The blue-skinned mutant has trained with Mossad and DARPA, making her one of the most skilled armed and unarmed combatants on Earth.
In X-Men: Black - Mystique, it is revealed that Raven Darkholme has memorised the location of the security cameras in every major airport in the United States. (Because she had free time, she also memorised half the ones in Canada.) With this knowledge, she can transform in public without it being picked up by the cameras.
Okay, she can't be detected by conventional means, but surely the X-Men's telepaths or Cerebro can find her, right? But that's not the case. In Uncanny X-Men #34, it is explained that Mystique's constantly shifting cells make it impossible to locate her. Even the greatest psychics have difficulty penetrating her mind.
Because of her tactical mind, fighting skills, and mutant powers, there is virtually no place Mystique cannot break into and no target she can't reach.