Q1 can't have A as its answer (otherwise it would contradict itself).
If Q1's answer was C (meaning Q4's answer was A), then Q3's answer would be C. However, Q2's answer should now be A, but this isn't allowed by Q1 (as Q4 is the first answer with A). This is a contradiction.
Therefore Q1's answer is B (meaning Q3's answer is A).
For Q2's answer to be C, Q4's answer would have to be A, which would contradict Q4. Therefore Q2's answer is B, making Q4's answer B. QED.