I was surprised by how successful Janice ____.

had became or became? They both sound correct.

It's "had become" since she became successful before "I was surprised" happened.

This is dealing with the sequence of tenses:
http://grammar.ccc.commnet.edu/grammar/verbs.htm#sequence

That is why I thought it was became, I can only pick

become
becomed
became
had became

I thought had become but I do not have that option.

had became = incorrect (simple past verb form never has a helping verb)

Among the others, "became" is the only one you can choose. What a bad question! Or a bad textbook/question writer!

Thats what I was thinking bad question.

Thank you.

If I were paying for this course from which all these questions are coming, I'd want my money back ... or something!

Both "had become" and "became" can be correct depending on the context.

If you are referring to a past event that occurred before another past event, you would use "had become." For example:
"I was surprised by how successful Janice had become by the time I last saw her."

If you want to describe a single past event without reference to another past event, you would use "became." For example:
"I was surprised by how successful Janice became after she started her own business."

In general, "had become" implies that the action happened earlier in the past relative to another past event, while "became" suggests a single past event without any specific reference to other past events.