d. for which I have been waiting all my life. This is the correct option.
The adjective clause is giving information about opportunity. We can rewrite the sentence like this : This is the opportunity. I have been waiting for this opportunity all my life . These two independent sentences can be linked into a simple sentence : This is the opportunity for which ( the relative word and the preposition have to be placed at the beginning of the adjective clause. Which stands for opportunity and for links the verb To wait and opportunity.) I have been waiting all my life.).
These options are not right:
a. This is the opportunity. ( This is the sentence without the adjective clause).
b. the opportunity for which ( This is incomplete. It has elements from the sentence and from the adjective clause).
c. the opportunity for which I have been waiting all my life. ( The adjective clause does not include the opportunity).
e. I have been waiting all my life. ( This is part of the adjective clause but it is incomplete).