答案：C
no matter who和whoever的最大区别在于前者只能引导让步状语从句,而后者既可引导让步状语从句（此时等于no matter who）,又可以引导名词性从句（包括主语从句、宾语从句或表语从句等）.
题中remember后面的宾语从句中,主语是一个从句____ sticks to his work,而谓语是will succeed,one day为时间状语.
很明显,选项引导的是主语从句,而不是状语从句（状语从句只能充当大句的状语）,所以只能用whoever,而不能用no matter who.
楼主可以试着体会这两个句子：
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.