The correct option is A But
The ideas in the two sentences are contrasting ones. To link two contrasting sentences, we use conjunctions like but, yet, still, while, etc. This rules out options B and D. Although both 'while' and 'but' are used to denote contrast, only 'But' makes a grammatically sound sentence in this question. If we place the word 'while' in this sentence, it will imply that the person 'got bruised at the time of completing the race' which is not what is required here. Hence, option A) But is the right answer.