答案：C
解釋：
no matter who和whoever的最大區別在於前者只能引導讓步狀語從句，而後者既可引導讓步狀語從句（此時等於no matter who），又可以引導名詞性從句（包括主語從句、賓語從句或表語從句等）。
題中remember後面的賓語從句中，主語是壹個從句____ sticks to his work，而謂語是will succeed，one day為時間狀語。
很明顯，選項引導的是主語從句，而不是狀語從句（狀語從句只能充當大句的狀語），所以只能用whoever，而不能用no matter who。
樓主可以試著體會這兩個句子：
No matter who sticks to his work, he will succeed one day.
= Whoever sticks to his work, he will succeed one day.
Whoever sticks to his work will succeed one day.