(A) is the only correct answer, and the others are so incorrect that a native speaker rejects them instantly, with no pause for thought. But here's the interesting thing to me, and I wonder if the other native speakers can "explain" this. It is only true because of the word "no." If you change the lead-in to "Under SOME circumstances," then A becomes grammatically incorrect, while both C and D become grammatically correct (while of course being factually untrue and very dangerous!) These are both correct: "Under some circumstances one should back up a motor vehicle even more carefully than usual." "Under some circumstances a motor vehicle should back up even more carefully than usual."

Under no circumstances should one back up a motor vehicle without looking carefully looking to the rear

Only one possible answer... what's your guess?